1) Sakura's Effect says "Injure this ninja, discard 1 card. Draw 1 card and this ninja gets the following effect 'At the end of this turn, heal this ninja'". It's a valid effect. Does that mean I can "injure this ninja" even though she is already in injured status and still activate the effect?
Sakura's effect is valid because if it wasn't she would be unable to heal herself at the end of the turn. You cannot Injure and already injured ninja.
2) If an effect says [Mission|Attacker], does that mean I can use the effect during my mission phase, then during the EOJ when i'm attacking I can use it again (all in the same turn)?
[Mission | Attacker] should be condisdered to be "During your mission phase". The attacker designation is a limiter that makes it only work on your turn.
3) Can you target something "not affected" by effects or jutsus? For example, if P1 uses a jutsu that says "The opponent gives 1 damage to one of their ninjas." and P2 picks a ninja with an effect that says "This ninja can only be damaged due to the results of showdown.", then is that a legal target or must P2 pick another ninja?
...Ok this one is more complicated.
Unless a card specifically says "This card cannot be the target of..." then you may target it with an effect even if it will fail. Now for the headache part:
If an effect stats "This ninja is unaffected by your opponent's (Ninjas, Missions, Jutsu, Client) Effects, or says this ninja cannot be damaged by your opponents (blah blah blah) effects that means your cards that let you do something dont work on them (give 1 damage, discard, ect...) this is true even if your opponent has to pick the target (Though there was a short time in the games history where this was not the case).
4) When a ninja's effect says "Heal target ninja" without actually specifying whether your ninja or your opponent's, then the ninja can be either one of your own or the opponent's right?[/quote]
Correct, unless there is a limiter on the target of the effect you may target any ninja that is a valid target (you can target a healthy ninja but the effect will fail, you cannot target a ninja with the effect "This ninja cannot be the target of..." if you are trying to target them with that type of effect.