On Q2, I really don't think that the player should be kept from shooting at all, just with that arm. Consequences are specific for a reason, and making it a direct impact on both sides is over general. However, if it was the person's main gun arm, you still have several options to go with. First, they probably ought to self-compel, but whether they do or not, I would say they can't use any gun-related stunts. Also, if they start to pull the gun and you compel them, I think it is perfectly reasonable to say something like "your arm shrieks in pain with your hasty movement and grip," then insert an appropriate penalty such as "your hand spasms open and your gun falls to the ground". If they choose to shoot with the other arm, that's fine, but you give them a penalty (-2?... I'd even go so far as to say drop their appropriate skill by two ranks unless they have an aspect that makes ambidexterity reasonable, in which case I'd reduce it by 1 instead) and again, they can't use gun-related stunts.
Meanwhile, unless I'm completely mistaken (which is certainly possible), NPCs can discover aspects just like PCs can. If a character is, say, dragging a leg, the NPCs could reasonably discover the consequence aspect and get a free tag for it. Similarly, they could get a tag when they see the character pull out the weapon, grimace, and drop it as discussed above.
Granted, this doesn't work if they NPCs in question already know about the consequence.