How much salt, add to tap water to purge bivalvia

In order:

1. No. It's possible, though not especially common, for a dead mussel to be stuck closed; they'll likely open with very little resistance.
2. 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.
3. 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:

1. 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.
2. 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.

Where I come from (Portugal) it is quite common to see in most restaurants and establishments shellfish being soaked several hours to even days long before consumption, especially sand dwelling shellfish, which is not the particular case of mussels.

The reason for this is that it keeps them alive and fresh for longer, while also purging any remaining sand or debris naturally found inside them, which is very common in burrowing shellfish, quite unpleasant to find when eating and can virtually ruin the dish.

These are however always soaked in either salted tap water at worse, or at preferably clean natural sea water from where they came from at best. Never just unsalted tap water, because this would obviously kill them quickly, and remove any natural salt that acts as flavor enhancer. Chlorine based disinfectants commonly present in tap water will also slowly affect quality of any living creatures (including aquarium fish) and may eventually be fatal them in the long run.

From your provided examples, most against soaking either state that tap water will kill them quickly, or considerably affect quality (which are both true); or is not needed for farmed shellfish.

I can't speak much for farmed shellfish, they are not as common here and quality may vary with providers and techniques, but even farmed one can some times be quite sandy.

So I'd say that soaking with either salted water or ideally sea water is at at worst redundant or not needed, but can be quite beneficial in some situations.

For farmed shellfish, if you find them clean and edible it is probably not needed, for "free range" ones you probably have more to gain by soaking than not.