To answer your first question, it is not there. Is that a function you use often? I may run a poll to see if that's something that a lot of users want (I'd check traffic numbers, but there's no "New Posts" URL, since it is technically a search query).

For the second question, I believe what you are seeing labeled as "Instant" is actually an indicator of the kind of notification you have set up. On mobile skin, the last poster's name is not shown in your subscription list.