Can fairies fly in an antimagic field

Yes.

There are no limits* to how high a pixie may fly, provided that they end their turn only one square above the ground. However, if they do end their turn above their altitude limit they fall with the consequences laid out for falling (1d10 damage/10 foot of drop).

*The theoretical maximum height a pixie may reach on their turn (with no extra movement trickery) is 8*3 + 1 or 25 squares high (run 8, trade standard for another run 8, action point for another run 8, +1 for starting height), that's 125 ft at the end of which they would fall. Falling says to subtract the creature's fly speed so that leaves us at 95 feet of fall, meaning 9d10 falling damage.

There are no rules in Pathfinder that prevent a creature from flying while wearing medium or heavy armor. However, armor does have some effects on flight:

• Fly is a skill affected by Armor Check Penalty – therefore heavier armors (which usually have higher ACP) make flying more difficult

• Medium or heavy armor slows the wearer – this affects flight speed just as it does other movement.

  • If your speed is not 30 ft., such as the 60 ft. flight you get from fly, use Table: Armor and Encumbrance for Other Base Speeds.

• Medium or heavy barding prevents the wearer from flying while carrying a rider – even if the mount is strong enough to carry the weight of rider and barding, there is a special limitation that prevents this.

These rules are, in my opinion, sufficient or even more than sufficient penalties for the heavier armors on flying creatures. Flight is an important part of the game; past a certain point, it becomes mandatory.¹ Furthermore, the classes which most depend on heavier armors usually already have the most difficulty getting into the air: Fly is typically not a class skill and they typically do not have class features that allow it. Because flight is so important, this is a major weakness of these classes, and they have to go out of their way (and typically spend a lot of money) to get it. But failing to do so, particularly for those specialized in melee combat, can make them incapable of engaging with their enemies, and even when they can it is a completely asymmetrical situation.

Therefore, I strongly recommend against houseruling this situation to make it harder for heavily-armored characters to get into the air. In fact, I would strongly recommend finding ways to make it easier, at least for those whose classes do not provide innate magic.

¹ Unless, by houserule or gentlemen’s agreement, no one is using it and the DM is carefully compensating for that.