Accidentally killed my mussels
In order:


No. It's possible, though not especially common, for a dead mussel to be stuck closed; they'll likely open with very little resistance.
Most likely yes. The main issue with eating dead mussels is that it's an indication they've been poorly cared for; you can't know how long they've been dead or how fresh they are. In your case, you know with reasonable certainty that they were alive until very recently so they're still fairly fresh.
No. Mussels open when cooked in order to "breathe"; the excessive heat overwhelms them and they're trying to vent a little bit (which cruelly just seals their fate, but we as cooks benefit). If they're dead, they won't have this reflex and they won't open on their own. As alluded to above, most of them will be partially open already.


I would still cook them, but do a couple things to be as safe as possible:


Cook them without further delay, within a few hours if possible. Any dead mussels will start to go south faster than live, since they're no longer respirating.
Discard any mussels that don't open after cooking. Chances are these were among the small contingent who stayed closed after death and you don't know exactly how long they've been toast. Better to play it safe and accept the loss; besides which, it's a bit of a chore getting them opened up when you've got plenty of their conveniently open brethren ready to eat.