Bugbear in the Playground
Re: Pathfinder Mounted Combat
Mounted combat in 3.5 is broken. I don't mean that it's too awesome to be allowed... I mean that the rules, as written, are incomplete, inconsistent, self-contradictory, and just generally do not work. Pathfinder re-upholstered a couple of the deck chairs, but didn't do anything to repair the iceberg rip below the waterline - most of the relevant text is copy-pasta direct from the SRD.
That said, as near as I can tell, the way it's supposed to work is:
Your mount acts on your turn, but gets its own actions, independent from yours, which it uses as directed.
If your mount is combat-trained, directing it is a Ride DC 10 free action ("Fight with a combat-trained mount"). The consequences of failing the check aren't clear, but best I can figure mean that you can still use your actions, but your mount won't be directed and so won't do anything useful. (This is not how we've been playing it. I need to talk to my GM about that. Not that it really matters for me... I've been able to Take 1 on DC 10 Ride checks since 2nd level, which is where we started.)
If your mount is not combat-trained, directing it is a Ride DC 20 move action ("Control Mount in Battle"), and if you fail, you spend the entire round trying to control it and can do nothing else, and presumably it does nothing useful either. (Note: not just your turn... presumably you lose AoOs and other out-of-turn actions for the round, too.)
In either case, you also have to make a DC 5 Ride check as a non-action or be forced to use one hand to control your mount.
If you succeed on whichever check to direct is relevant, your mount will then use its actions as directed - move and attack, charge, whatever - and you can use your (remaining, if you had to use a move to control a non-combat-trained mount) actions however you want.
There isn't much guidance for how these two sets of actions combine.
You are explicitly restricted from making more than one melee attack if your mount moves more than 5' (note: not necessarily a five-foot-step), unless you've got the Mounted Skirmisher feat (or three levels in Wild Plains Outrider, in 3.5), which extends the amount your mount can move and you still full-attack up to its single-movement. This seems to apply to any movement (e.g., your mount charging for less than its single-move distance), not necessarily just a single move action. Sadly, my GM has forbidden me from using this to make a Spirited Charge full attack with a lance, even though, AFAICT, it works. Insofar as Spirited Charge works at all, anyway.
You're explicitly able to make a ranged full attack while your mount is moving - single move, double move, or even running - at various penalties depending on how fast it's going... no penalty for a single move, -4 for double, -8 for running. Mounted Archer halves those penalties. (As a professional mounted archer, I don't think it's worth it. My wolf can move 80' as a single move and I still can full-attack without penalty... why do I want to waste a feat slot on this?)
Similarly, you're explicitly able to cast a spell while your mount is moving, with varying Concentration DCs depending on how fast it's moving. The descriptions for the check DCs are a little vague, but I figure they break down similarly to the ranged full attack penalties... if your mount single-moves, you can cast before or after its movement without a check, if it double-moves, you have to make the DC 10+(spell level) check for "vigorous motion", and if it's running, you have to make the DC 15+(spell level) check for "violent motion".
When you make a mounted charge, it's your mount's full-round action being used for the charge, not yours. This means that Spirited Charge and Ride-By Attack don't technically work, because the conditions in which they take effect are never fulfilled (and Ride-By is additionally almost always defeated by basic geometry requiring you to continue the line of your charge through the target's square), but the intention there is pretty clear. But anyway, because the mount is the one making the charge, it's not only allowed but required to make the attack at the end of it. The rider has the option of attacking, and gains charge benefits if he does (and charge penalties regardless), but doesn't have to. There's nothing to indicate that the rider's optional attack isn't an ordinary standard-action attack, so he should be able to use his move action for something else if he wants.
(My current character is a mounted archer with a sideline in mounted charger... it's pretty common for me to decide shootin' time is done and I want to stick a 10' pole through some poor sucker, and have my dire wolf charge, draw my lance as a move action on the way in, and make my attack - with all the benefits of a mounted charge, which with Spirited Charge and a lance are substantial - at the end as a standard action. And then the wolf bites them, also with all charge benefits - which include Powerful Charge - and tries to trip them, and we either Ride By and stop out where we can do it again next round - or I can take another move action to put the lance away and resume shooting with the bow that's still in my off hand - or stop there so we can make AoOs when our victim tries to get up.)
I have a kind of unspoken agreement with my GM that I don't exploit the hazy areas in how the action sets interact in ridiculous fashions (e.g., mount my dire wolf as a DC 20 free action, guide it with my knees as a DC 5 non-action, so I don't need to use a hand to direct it, as a DC 10 free action, to use its full-round action to run 400', while using it as cover as a DC 15 non-action, dismount as a DC 20 free action, and then use my own full-round action to charge 80' and attack with my saber (only once, obeying the letter of that rule), thus covering more than four range increments for my bow with a melee attack... and note that I'm +18 on Ride at the moment, so all but the first and last checks are auto-successes, and I fail those only on 1s... next level those will auto-succeed too), and he lets me use my judgment as to what constitutes a ridiculous fashion.
The Mounted Combat feat in 3.5 is restricted to once per turn, but doesn't seem to actually take an action. Pathfinder has made it a swift action that can be used reactively like an immediate action, which is weird enough, but then added the Trick Riding feat, which as one of its effects allows you to use Mounted Combat twice per round. It doesn't say how that's supposed to work, action-wise, but I figure the first use burns your swift action, but you're then allowed to use it a second time during the round for no additional action cost.
Spirited Charge and Ride-By Attack, as mentioned, don't technically work, because when you make a mounted charge, you're not using the charge action - your mount is. It's pretty clear how they're supposed to work, though.
I don't know what's supposed to happen if you Trample something with a mount that doesn't have hooves... it can be read as it's out of luck and doesn't get anything, or that it gets a hoof attack anyway... We've figured it gets a size-appropriate slam attack as a secondary.
Pathfinder didn't fix the contradiction between mentions of the lance mechanics, where one says you get the multiplied damage when charging on any mount, and the other says only that you get it when charging on horseback...
Um, anyway, short answers to your questions:
Your mount gets its own actions during your turn. It can use them normally, but you have to direct it to do so. If it's combat-trained, this is a DC 10 free action; if not, it's a DC 20 move action that becomes an all-consuming one-round occupation if you fail the check. The action costs are both for you... being directed is not an action for your mount.
If your mount charges, it's using its full-round action to do so, and must attack at the end of the charge, as per the usual charge rules. The rider has the option to attack as a standard action, and gets the benefits of the charge if he does. Both always suffer from the penalties of the charge.
Play your character, not your alignment.