I think your group is over thinking it a tad. Do what is awesome.
With regards to 1 - Your character can fly however they please within the maneuverability and speed granted by the spell. Saying someone gets cover below you because you have to shift upright to attack? C'mon, that's ridiculous. Unless you have thrown in some Unearthed Arcana or are houserulling it, there is no facing. Give the person higher up in the sky a +1 to attack (from higher air, hehe), and call it a day.
With regards to 2 - Ride checks get bumped up a bit, but if this Paladin is intent on mounted combat, he should already be acing the lower DCs by 5th, no problem. Like others said, falling is still possible with being unhorsed, or if he just so happens to fail a Ride check. The special mount is just that, special. If I was the Paladin, and that horse was my "schtick" I'd be a little peeved that this excellently battle-trained warhorse, that has a seemingly otherworldly bond with me and is the target of (presumably) other spells has to essentially sit it out. Risking a fall is enough of an equalizer at the end of it all. A flying horse with a Paladin on it is awesome. Just do it.
With regards to 1 - Your character can fly however they please within the maneuverability and speed granted by the spell. Saying someone gets cover below you because you have to shift upright to attack? C'mon, that's ridiculous. Unless you have thrown in some Unearthed Arcana or are houserulling it, there is no facing. Give the person higher up in the sky a +1 to attack (from higher air, hehe), and call it a day.
With regards to 2 - Ride checks get bumped up a bit, but if this Paladin is intent on mounted combat, he should already be acing the lower DCs by 5th, no problem. Like others said, falling is still possible with being unhorsed, or if he just so happens to fail a Ride check. The special mount is just that, special. If I was the Paladin, and that horse was my "schtick" I'd be a little peeved that this excellently battle-trained warhorse, that has a seemingly otherworldly bond with me and is the target of (presumably) other spells has to essentially sit it out. Risking a fall is enough of an equalizer at the end of it all. A flying horse with a Paladin on it is awesome. Just do it.