So, you want a Japanese 360 to play the region locked and upcoming NTSC-J releases which are bound to be also region locked.
Here's what you need to know...

- Can I modchip/hack/firmware change/modify my Xbox 360 so it can play NTSC-J games/copies?

No.

- How can you tell the difference between console versions?

If you're ordering online (which you most likely will be), you can't.
There's nothing wrong with owning a Jasper unit over a Falcon,
nor is there anything wrong with owning a Falcon over a Jasper.
Common sense and recent reports (http://www.theregister.co.uk/2009/09/03/squaretrade_console_failure_report_sept_09/) suggest that owning the latest model of the console holds the advantage.
A notable advantage which the Jasper has is the on-board 256MB RAM to cover the NXE update
which requires a memory card or HDD in Falcon or previous models.
Differences between Falcon and Jasper units can be found here (http://en.wikipedia.org/wiki/Xbox_360_hardware).

Apart from purchasing an Japanese 360 physically,
there's no way to tell which unit you will be receiving.
You could always try emailing Play-Asia but that will probably get you nowhere.

- What are the benefits of owning a Japanese 360?

Most Shmups and other very Japanese-esque games are region locked, and this grants you access to all of them.
A majority of NTSC-J games also end up receiving an Asian English release, but not all.
Some of them even come out in English before the US, like Blue Dragon or Lost Odyssey.

- What are the disadvantages of owning a Japanese 360?

Some games like Culdcept Saga, Eternal Sonata, Earth Defense Force 2017 and Operation Darkness are region locked to US (NTSC/UC) only.
They have Japanese releases, but of course they're all in Japanese.
Some games have Asian English releases, like Eternal Sonata for example, but some don't.
Eternal Sonata aside, all the others are Japanese.
There's a possibility that worthwhile games in the future will be region locked to US only,
and you won't be able to play them.

- Is 'x' Xbox 360 game compatible with a Japanese 360?

Region compatibility guide is here (http://www.play-asia.com/paOS-00-3-xbox360_compatibility_guide-49-en.html).

- Is 'x' Xbox game backwards compatible with a Japanese 360?

Backwards compatibility guide is here (http://www.xbox.com/ja-JP/games/backwardcompatibilitygameslist.htm).

- Can I create a US account on a Japanese 360?

Yes.
Just use a US address and a US specific passport account.
I would recommend making an account of your own region, and a Japanese account.
If you use a non-Japanese account and a game tries to access the JP store,
it will give a "service is temporarily unavailable" error.
There's details on how to create a JP account below.

- What Shmups are available, and what Shmups are coming to the Japanese 360?

Released:
Shikigami no Shiro III - Dec 12, 2007
Raiden Fighters Aces - Mar 25, 2008
Raiden IV - Sep 30, 2008
Otomedius Gorgeous - Nov 19, 2008
Dodonpachi Daioujou Black Label Extra - Feb 19, 2009
Shooting Love 200X - Feb 19, 2009
Death Smiles - Apr 24, 2009
Mamoru-kun wa Norowarete Shimatta - Jun 25, 2009
Raiden Fighters Aces - Nov 19, 2009 (Games on Demand)
Mushihimesama Futari (region free) - Nov 26, 2009
Raiden IV - Jan 14, 2010 (Games on Demand)
Aegis Wing - 2007 (US Marketplace only) (Xbox Live Arcade)
Ikaruga - 2008 (Xbox Live Arcade)
Triggerheart Excelica - 2008 (Xbox Live Arcade)
Omega Five - 2008 (Xbox Live Arcade)
R-Type Dimensions - 2009 (Xbox Live Arcade)

Upcoming:
ESP Galuda II - February 25, 2010
Ketsui - TBA, 2010
Death Smiles II - TBA, 2010

- Where can I purchase one from?

Basically, the cheapest place to get a brand new console from is Play-Asia (http://www.play-asia.com/paOS-14-71-bq-49-en.html).
They vary in price, models, colors and bundles.
Note that some sites like Yes-Asia deviously include their shipping cost inside their items price,
but if you wish to shop elsewhere, do so at your own caution.
Ideally, getting help from someone in Japan would be the cheapest route.

- What if it dies?

It entirely depends on your location, but most have it taken in to be repaired.
One guy's was sent from New Zealand, where it was then sent to Australia,
where it was then repaired and sent back.
Some parts of the world will not allow you to have your console repaired.
Sometimes they will replace consoles with working ones, so make sure that if yours dies,
that they've made a note not to replace your unit with another, as it's most likely going to be a unit of your own region.
Microsoft have announced that they will cover dead 360 systems even if they don't have the RRoD,
and no additional charge is given.
It can take anywhere up to a month to successfully get through the repair process (depending on distance, and work load).

- What are the differences between the Japanese and US marketplaces?

The JP marketplace severely lacks in content in comparison to the US one -
but has exclusive content which I'll list in more detail below.

- What about DLC? What can I do with it?

Most of the DLC available is region locked as well, so this means you won't be able to purchase DLC inside Japanese
games when using an American account unless the game and content is the same and is uploaded to the US marketplace's servers.
Outside of games, you can purchase DLC at the marketplace by using points,
providing you either have a credit card or points voucher.
Points are also region locked, so American point cards won't work with Japanese accounts. Points can be bought from here.
As of late 2007, it's no longer possible to add a foreign credit card to a Japanese 360 account,
but existing foreign credit cards on JP accounts will still work.
READ: The brief period when NXE was launched where you were able to use foreign credit cards has ended.
It's once again impossible to use a foreign credit card on a Japanese account.

- Will required patches for Japanese 360 games work if I log in with an American account?

Patches automatically download when you load a game regardless of your region.
But in-game DLC, such as purchasing the ships and themes inside Raiden IV, will not work when playing the game on a non-JP account,
as the DLC isn't uploaded to those marketplaces.

- What about voltages and power supplies?

360 consoles use external power, so you can use a power supply in your
own region on a foreign console without any need for conversion.

- Ok, so how do I get a Japanese 360 account?

After selecting to get an account, it will display 4 steps.
Choose "Sign Me Up".
Afterwards, enter your email, then enter your password.
It will also ask for your date of birth, probably to filter stuff for people under 18.
After this you should be on "Verify information".
Locale determines which marketplace you're going to sign up for, so choose Japan.
Accept the Terms of Service. If it's not in Japanese, go back and do it again.
After accepting the terms, it should prompt you with a menu displaying what Xbox Live offers.
Click "Continue".
Choose "I don't want a gold membership", and it should say that you're eligible for 1 month of Gold.
(this can only be done three times per console)
Continue.
It'll ask you if you wish to add payment info, choose "No, add it later."
Now it'll ask for your first/last name, phone number, and contact email (which should already be there).
Next it'll ask you if you wish to sign up for "exclusive insider information",
and the bottom choice asks if you wish to share your information with partners.
I assume the top option just sends you email junk and the bottom option registers you on MyGamerCard.
But since I dunno, choose whatever and click "Continue."
Select a GamerZone - Recreation, Pro, Family, or Underground.
Past a few menus, it'll ask you to choose a GamerTag, which will be your online identity.
READ: If the GamerTag is available and you choose "OK", it'll proceed to create it immediately.
If it isn't available, it'll ask you to try another GamerTag.
And you're done!
Choose an avatar thing and have fun. ^o^

- So now that I have one, what can I download?

Whatever's free, basically.
There's a bunch of free gamer icons for Puyo Puyo Fever on the marketplace, plus a few others for Xbox Originals.
There's a Raiden Fighters Aces demo as well.
But really, not much unless you get yourself some points.
There was a time where some demos were Japanese marketplace-exclusive,
like Ninja Gaiden 2 and Eternal Sonata, but that's long gone.
You can also freely download a bunch of trailers, for games like IDOLM@STER: Live for You or Agarest Senki.

- Great, but what Shmup related material is available exclusively to the Japanese marketplace?

Current titles:
Senko no Ronde (旋光の輪舞 Rev. X): Gamerpics, themes, outfits
Shikigami no Shiro III (式神の城III): Gamerpics
Raiden Fighters Aces (ライデンファイターズACES): Gamerpics, themes, available on Games on Demand (IP-locked)
Raiden IV (雷電IV): Gamerpics, ships, themes (pre-NXE)
Otomedius G (オトメディウス ゴージャス!): Background music, premium theme, gamerpics, new characters, new stage (Moai stage)
Daioujou BLEX (怒首領蜂 大往生・ブラックレーベル EXTRA): X-Mode replay
Death Smiles (デススマイルズ): Trailer, gameplay trailer, gamerpics (characters), gamerpics (enemies), premium theme (bath scene), Mega Black Label
Mamorukun ha nowareshimatta! (まもるクンは呪われてしまった！): Trailer, gamerpics, two new characters
Shooting Love 200X (シューティングラブ２００X): Theme, gamerpics
Mushihimesama Futari (虫姫さまふたり): Theme, promotional video, Black Label

XBLA:
R-Type Dimensions (アールタイプ ディメンジョン): Game (1200 points), premium theme, gamerpics
Ikaruga (斑鳩): Game (800 points) non-premium theme, gamerpics
Triggerheart Exelica (トリガーハート　エグゼリカ): Game (800 points)

XNA:
Crescendo Symphony: Demo, full game (240 points)
Ultimate Sacrifice: Demo, full game
X-Over: Demo, full game

All of the above will cost points (remember, points are region locked) if you wish to purchase them.
As it stands, the current Shmups available on the Xbox Live marketplace aren't exclusive.
Aegis Wing is free, but only available on the US marketplace.
The rest (Ikaruga, Omega 5, Trigger Heart Exelica and so on) can be purchased worldwide.

- Can I use a Japanese account for online gaming?

Only if you add points and get yourself Gold status, which costs money.
But it'll work the same as any other account.
Japanese points can be bought from Play-Asia.
Xbox Gold memberships are region free, but points are region locked.
Note that if you add your credit card to any Xbox Live account,
you can't remove it unless you phone Microsoft's horrible customer support and have them manually confirm it.

- What are some currently region locked Japanese exclusives for the 360?

All Japanese exclusives are region locked with the exception of Mushihime-sama Futari.
Non-exclusive region locked titles exist like Senko no Ronde (released worldwide), CLANNAD (multi-platform), and Shikigami no Shiro III (multi-platform).

- What about the dashboard? Can that be changed?

The dashboard can be changed into any language, but having and using a Japanese account will mean
that marketplace related items will be in Japanese, while the rest is in English.
Bringing up the guide button while having an English interface,
and moving to the far left tab will allow you to navigate the marketplace in English.
This won't change the marketplace's language,
but at least you can easily get to sections of the marketplace via this tab.

- Is it worth waiting for 'x' game to be localized instead of buying a Japanese 360 for it?

Only if you're happy knowing that there's other people out there playing a game that you want to play,
simply because you don't want to import it.

- Can I exchange 'x' accessory from 'x' region to another region Xbox 360?

Yes, no console accessories such as memory units, headsets, HDDs, etc.
have region locking so there's no need to worry about that.

- I have a currently in-use HDD. Can I use it with a Japanese 360?

Yes, but you would need to use the Xbox 360 license migration tool (http://www.xbox.com/en-US/support/systemuse/xbox360/licensemigration/), otherwise you won't be able to play
your arcade games on anything but the account in which they were originally purchased from.

- What if I download a game from the Japanese marketplace? Won't it be in Japanese?

This depends entirely on your language settings, only rarely on the game itself.
So downloading Trigger Heart Exelica and using an English setting means that it'll still be in English.
Though some games will default to Japanese automatically, such as Marvel vs. Capcom 2, if your console is Japanese.
Capcom XBLA titles do this in particular.

- How do I change the location in my profile?

Set your Locale to Japan and it'll change your profile (where your motto goes) and will appear there if you don't have one set. It will also appear briefly behind your motto.

- Can I purchase Japanese-only games via the Games on Demand service using a JP account?

No.
The games are IP locked, so you can't download them even if you have a JP console,
JP account with points attached, and/or JP credit card attached as well. I've tried.
It simply will not work.
If you attempt to purchase via points, it will say "This content is not available in your current location."
And if you attempt to purchase with a credit card it'll just tell you the exact same thing.