Throughout the game, there are lots of characters who are dead, for example seymour, auron, mica, and belgemine. It seems that these people act normally like real people, so how come other people who die can't do the same. And if when you die you can still act like normal, why would people fear death?

Because not all people who die in the game have this option.

The dead people that you see were only dreamt up by the Fayth and therefore did not choose to be there. The were dreamt up specifically to destroy the dogmatic Yu Yevon and save Spira from another vicious cycle of terror and ruin.

The only place where people can choose to meet their departed loved ones is in the Farplane.

Because of this, Tidus was really really upset when he discovered that Yuna had to sacrifice her life to defeat Sin.

The People that you see in this game are the Unsent; People who, when they died were never sent to the Farplane and are Forced to stay in the Living Relm.
Usually in the Example of Seymore and Auron, there deaths were somewhat unnatural. Then there is Maester Mica that decides to Cling to the living so that he can stop Yu Yevon from destroying the world. All have forsaken the option of being sent

This always confused me about X: how the hell can there be 'unsent' if, as someone says near the beginning of the game, people who aren't sent become fiends? Maybe I just can't remember the explanation, if one was given, or I've just got the whole thing wrong (never paid that much attention to it), but...

IIRC, the unsent turn into fiends if there were certain circumstances surrounding their death that left them with bitter, sad feelings.

And if there aren't bitter feelings they just become normal unsent like Auron? There seem to be lots of benefits to being unsent, i.e. being immaterial.

The explanation was given in the game.
1). Those that are unsent usually start having bitter feelings for the living and become fiends to destroy life.
2). Self-Explanitory: Seymours purpose to being unsent was to give Spira the so-called "release from pain" (and planned this while he was alive) and merge with Sin with Yuna "helping him" The fact that he wanted to "help" Spira, he became an Unsent.

When someone dies, one of three things happen.

- They get sent to the Farplane.
- They become fiends.

OR

- They become 'Unsent', which only happens when a strong emotion binds them to Spira, such as:

Auron's promise to watch over Tidus,
Seymour's hatred and wanton destruction of Spira, or
Belgamine's urge to help new Summoners.

When someone dies, one of three things happen.

- They get sent to the Farplane.
- They become fiends.

OR

- They become 'Unsent', which only happens when a strong emotion binds them to Spira, such as:

Auron's promise to watch over Tidus,
Seymour's hatred and wanton destruction of Spira, or
Belgamine's urge to help new Summoners.

Ah, OK, that's makes sense now. Well, as much sense as it's going to make.

Ty, I think it makes sense now.
Although it would be interesting to try to cheat the system by dying with a strong emotion.

It is very complicated, but Auron explains most of it while sharing the hanging prison with Tidus, and the rest upon the discovery of his condition.
If you pay attention to what Seymour says (I know, its hard considering his whiney bitch voice), you can also pick up little bits here and there that can help explain it all.