Ok...so it's a little longwinded about Death in 6x11. I'll put it in the info :)

My assumption would be what you stated, though I don't really know for sure. Probably the fact that Lucifer summoned him and made him walk amongst the mortals is why people could see him. He had to take on a human form since he was summoned. Probably why everyone could see him then, but that is just a guess...somebody else might know for sure.

As far as Dean having to touch people while Death only had to twist the ring, again it's only an assumption, but I would consider that since he is Death, and has been around, as he said, at least as long as God, if not longer, he has powers that Dean could never possess, even with the ring. I don't think Death necessarily needs the ring to kill people, I think it just concentrates his power or something like that.

Anyway, sorry if all that was absolutely no help, but that's what I thought. :))

I'm not sure but maybe Death can control when you see him and when you don't or who he wants to appear to? It might also have something to do that when Lucifer summoned him and Death was bound, he was trapped by a physical form and was made to go where Lucifer wanted him to go, but now that he's free he doesn't have a physical form anymore and instead appears to Dean in a form that he is familiar with

I could be wrong but I don't think they've ever actually address that question at least not that I've heard of