Ranger feats and animal companion Feats questions

[Seba777]

Hello everyone, I have a few questions as a first time player.

I am a level 4 Human Ranger with Combat style feat Archery,
Could I have chosen both Deadly Aim and Rapid shot at level 1 (with enough dexterity and base attack bonus) without having any Combat Style yet?
At level 6 when I choose Combat style Crossbow for example, will I be able to choose 1 bonus feat of each of the combat style chosen?

Now the animal companion questions:
Can I choose to have a Giant Vulture as a companion? Would he keep the Diseased special ability (active when doing melee attacks)?
Would he keep the +7 Flying and +13 perception skills? What about the feats listed in their page (like Toughness)? Would they only be "activatable" by leveling them?
(In case a giant vulture wouldn't be possible, the same questions would be for any other working companion too).

Thanks for the help in advance, I know they are many question but I find this game/wiki kinda confusing when combining different abilities/feats.

[avr]

Rapid shot has a prerequisite of BAB +2, you can't take it at level 1. The feats a ranger gets via their combat style can bypass prereqs (but not others like those you get at levels 1, 3, 5 etc.) and they get their first combat style feat at level 2 and their second such feat at level 6.

Animal companions don't use the bestiary stats and abilities. They use the numbers and special abilities from the table in the druid section and the stats and extra special abilities noted for that particular type of animal companion.

If you're a 4th level ranger with no relevant feats, archetypes, racial abilities etc. then you use the 1st level line of the table since rangers get animal companions at level -3. 2 skill points which you can give to fly and/or perception if you choose, and one feat which could be toughness or something else. It is possible to get a giant vulture, details here - no diseased ability sorry. Presumably your ranger keeps it healthy.

[Coolwasabi]

Rapid shot doesn't have a BAB prerequisite, but it needs pointblank shot.

The crossbow style gives you a feat at 2nd and 6th level of ranger without any prerequisites needed. The 2nd level can be deadly aim, focused shot, precise shot, and rapid reload. At 6th level it can be any listed for 2nd and adds crossbow mastery and improved precise shot as choices.

[avr]

Coolwasabi's right, no idea where I got the +2 BAB required from.