I fought Garuda and nothing happens when I killed it, is that normal?

Can you miss Espers like FFVIII when some ppl missed few summons?

A few are in the storyline, and the rest are extra side quests that you have to take. So it is possible to miss them if you just don't do them, but I'm sure you can do them anytime.

And yes, you can summon espers and Garuda is not one of them.