A couple questions about normal flying creatures (summoned eagles and what not).

So I have been looking around for info to make my Pathfinder game go by the rules as much as possible for once, to learn the "real" mechanics of the game.

I was looking at posts about summoning Eagles (Summoner Monster I) or an attacking Quasit (0 reach) and if they could occupy the same square as the creature they are attacking or not, or if they are supposed to enter, take an AoO to the face, attack, and then move (automatically) out of the square, and having to take an AoO the next turn when entering again to make use of their 0 reach melee attacks. I'm still unsure about this, so feel free to share your knowledge/opinion on the matter.

Anyway... What surprised me is that I just found out (from some sightly unrelated comments) that you are supposed to make Fly checks if you take damage (to avoid losing height and falling to the ground) or if you are trying to "hover" (aka, staying in there to perform Full Attacks on the next rounds) and I do wonder... Do you guys usually use these Fly check rules? Up until now I just summoned a flying eagle and assumed it just moved normally but flying, but apparently it has to move at least half its movement or do a Fly check, or can fall to the ground after being attacked and failing a Fly check and what not... Anyone care to enlighten me a little? Do you guys use all these flying checks for "normal fights" with "normal flying creatures" that are just attacking (and being attacked) by things in the ground, like a Quasit that goes to melee, or a summoned Eagle that is ordered to attack and the likes? What kind of penalties/problems does an Eagle (or any creature) falling to the ground suffer? They generate AoO when trying to get in the air again? Lose an action? Movement? Do you guys use the Flying rules at all? Should I just ignore them for the time being? Couldn't (by the rules) a grounded eagle adjacent to an enemy just take a 5-foot-step and still do a full attack from the ground (lol!)?