1. Yes you can move yourself whilst the ball in the air, but usually the defender is in the position where the ball is going to land, so the only thing you can do is to try and move towards the defender, maybe push him back. If you move forward you wont get the ball coz it will be too high when it reaches you.
2. usually if you want to cross after you have passed the penalty areas lines (not gone inside, but you are parallel with the penalty area, but you're still on the wings, if u know what i mean) you need to press either up or down first and then press the cross button. this allows you to center the ball and is usually going for one of your players, provided they are in the box. you can press the direction towards the box for a far post cross, or press the direction away from the box (depends if your left or right of the box, up and down have different effects) to perform a near post cross (this is particularly useful if your players are slightly closer, and usually this should be prefered IMO, because the speed the ball is at makes it easier to head it in, but unless your player is quite far away from you, then press the toward-box directional button for the far post cross.)
if you haven't become parallel with the box, and want to cross it into the box, press L1 + O (or whatever your cross button is, mines square) to perform an early cross. this isn't the best thing to do, but if you don't have time or your player is in a mile of space, and isn't offside, then its a good option. You can just hold O and point (with your analogue or dpad) the direction u want the ball to go in. this is useful if you want to pass the ball to someone not in the box, but somewhere with space, and you couldn't do it with a normal pass because it would be intercepted.
To header, just press the shoot button and the direction the ball should go, and if your lucky it should go in, but it all depends on the cross, the players ability to header, the angle the cross catches the players head, the goalkeepers ability, because rarely the goalkeeper or a defender (standing on both corners, as seen on TV) can block it sometimes. Im not sure, but i think there is such thing as controlled headers as ive practiced it in training mode and it seems to go in more than a normal header. to do a controlled shot or header, just press and hold the shot button, and whilst its filling up to the amount you want, hold R2 and the direction you want the ball to go (according to the goal, so even if you do quite an extreme right, the player should go for the right of the goal, even if he misses by a bit) and let go. the player usually uses their inside foot to shoot, and it isn't as powerful or fast as a normal shot. you should use this shot when your in a situation where a normal shot would send the ball flying or otherwise wouldn't work.
3. Overhead kicks and those amazing kicks your talking about don't need special buttons, but a special situation. you can never be sure what the player will do, but whenenver you feel you should shoot, just shoot (unless your 1-0 down in the cup final in stoppage time!!) and once in a while your bound to do these amazing shots. generally for overhead kicks, the player needs to be in a position where the ball is directly above him and he has more or less his back to the goal. its something like that, ive only had one successful overhead kick (rooney, who else

) and thats what happened then, so just keep trying to shoot, and your bound to strike some amazing goals.
hope this helps.