[RPG] the maximum (air speed) velocity of a pixie

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.

Given that you appear to have all the rules already, it seems that the problem is in interpretation. Given that, my view is :

1. Should the mounted PC be treated as a normal mount for a PC, losing his turn and becoming subordinate to the rider?

   • Answer: No. The mount is the same level and equal in power

2. If 1 is "no", do they share initiative counts?

   • Answer: No. They each roll initiative, and act on their turns. If one wants to move and the other doesn't, then the rider either dismounts (if the rider is the source of the move) or falls prone (chosing not to move with the mount). As a generous DM I'd allow an acrobatics check to avoid falling prone.

3. If 1 is "no", can the rider use his move action to make the mounted PC move, or force the mount to act by spending his own actions in any other way described by the Mounted Combat rules?

   • As above; if one wants to move an the other doesn't, then it's either a dismount or a fall-prone for the rider, depending on who's turn it is.

   • Per the comments; the mount should only be able to be move normally once per round - whichever commands the mount uses their move action to move, the other still has a move action but can't use it to move (unless it's the rider dismounting). Clearly other sources of movement (e.g. warlords) would still have the expected result - and the mounted combat rules cover that sort of thing already.

4. Can the mounted PC use the rider's base skill check bonuses as described in the Mounted Combat feat (e.g. a human with a pixie on his shoulder uses the pixie's Stealth modifier)?

   • If the rider has mounted combat and the mount is willing, then I would go along with this.

5. How would feats like Holy Steed, which gives a rider's mount bonuses to defenses and damage, be applied?

   • I would go along with this. As a DM, I'd much rather my players bunch up than spread out. A small bonus is worth the penalty.