Before I answer your questions, here something you must always remember:
You can't make the same action more than one time. So: You can't attack, move and than attack.
1. If you have 3 actions, you could attack (no penatly, because it is your first action), move up to your full movement (-25 penalty, if you must make a test) and after this, make a notice check (-50 penalty)
2. You can only spend 1 action on movement. If you move first and than attack, the attack action have a -25 penalty, if you attack first and than move, a movement check (for example "athleticism" to run further or longer time) would get the -25 penalty
3. AFAIR is a counterattack a passive action, so you could make it, if you aren't put on defense. But: You have a pool of "additional attacks" (for every full 100 points in your attack ability, you have one additional attack), and I think, your counterattacks use the same pool. So there is something special: All your attacks are getting a -25 penalty for every additional attack you make.
For example: You make one attack action (you are not allowed to make more per turn), with two attack, both attack would get a -25 penalty, because you make one additional attack. If you had made a move action before, your attack action would get a additional -25 penalty, so all your attacks would get a -50 penalty (-25, because your attack actions is the second action and -25 because you make an additional attack).
4. You can counterattack as long, as your "attack pool" isn't emtpy, but usually you must say the numbers of attacks, which you will use this turn, before you roll initiative. My groups plays a little different: You must say the number of attacks the moment, you use your first attack.
For example: Hasib, a acrobatic warrior with an attack ability of 225 (which means, 3 attacks), can counterattack an enemy. He can decide, he will use only one attack (so, after this counterattack, he can't (counter-)attack in this round again, but he wouldn't have a penalty for additional attacks, or he could decide to use 2 attacks (one for the counterattack and one for later), so both attacks would get a -25 penalty, or he could use all 3 attacks, all with a -50 penalty. But: he can only counterattack with one attack (so if he would use 2 attacks, he couldn't make to attacks for one counterattack).
5. Like said in the beginning: you couldn't make the same actions more than one time per turn. So you can't move three times. But: If you would make 4 different actions (move (0 penalty), search (-25 penalty), use a active spell (-50 penalty) and than attack (-75 penalty). And: There is something like a charge maneuver, on page 84 of the core book (called "Charging").