Welcome to the forum, Calcor 
@Calcor:
1. During the combat move phase, I don’t have to attack with all units I have on the region, right? For example if I have 2 Tanks, 2 Inf I could only attack with 2 tanks and let the inf there, right?
Yes, you are free to move as many units into the enemy territory as you want.
@Calcor:
2. If I win a combat - do all attacking units have to move in the new captured territory?
Actually the units are already there, as you moved them there during combat move phase. They have to stay in the captured territory and are not allowed to move during noncombat move phase.
@Calcor:
3. During a bombing raid - I know that the escorte and defending fighters will roll a dice wether they hit an airplane or not, but does the bomber also has an attack role in this combat round?
Yes, see:
@rulebook:
- The attacking bombers and fighter escorts and the defending fighter interceptors will be the only units participating in this special combat.
- The combat lasts for only one round.
- All of the air units have attack and defense values of 1.
@Calcor:
4. If someone attacks me in their round, can the then defending units in my turn use they combat movement and everything just normal?
Because when someone attacks me and I scramble with planes I understand that these airplanes are not allowed to participate in my upcoming battle phase, right?
Scrambling is a defender’s move during the attacker’s turn. Scrambled units can not participate in another battle during the attacker’s turn.
So in their upcoming own turn they are not restricted.
@Calcor:
5. Transports. As far as i understand it takes one round to load my units on a transport and a second round to move and have an amphibious assault?
No. You may load and unload during Combat Move Phase (Amphibious Assault) or during Noncombat Move Phase (into a friendly territory), too.
You may load during NCM and unload for an Amphibious Assault during CM of your next turn, too.
When you load onto a transport of a friendly nation, your ally moves the transport on his turn, and you unload on your later turn.
@Calcor:
6. Submarines Surprise Strike. If I get to choose the surprise strike, I am not allowed to participate in the normal combat again? If the attacker presses and no destroyer is there, do I have another surprise attack?
Your submarine shoots one time during every round of combat. Either as a surpise strike (no enemy destroyer present) or during regular combat (enemy destroyer present). The surprise strike is granted in every round of combat, provided no enemy destroyer is present.
HTH 