the chances of there being a Dark Souls 4, 5, 6 ect within short succession after this are pretty unlikely.
pretty obvious DS3 is meant as the "finale". maybe From will eventually go on to do another, but that won't be for a very long time
I don't think so. If you include Demon Souls, then you have basically 4 (Souls) games.
They'll probably do another souls type game like bloodborne, creating and using different worlds and settings.