No. TES should never go multiplayer. Ever.
I don't think so. I think Mass Effect 3 has the right idea. Keep the single player entirely isolated and give it the full treatment, then let another studio use the engine and game systems to create a similar, but separate experience for multiplayer. Deathmatch wouldn't work and honestly is against the spirit of the game, but similar to what ME3 is doing, cooperative play would work extremely well in this type of a game. Crawl some dungeons with your friends, level up your character, collect some loot. Basically a Diablo II styled mini-game within the next TES package.
Don't even tell me that Bethesda wouldn't make a ton of money off that. Skyrim has done well and I think the next game will probably be damn solid as well, but being able to bring in more $$$ = more money is able to be reinvested into the game later, so that stuff like bugs can be fixed.
@ the OP's suggestion: No. At multiplayer in general: If it is done right.