There's no canon answer on these that I've found, but a ghost is defined in canon as an "imprint of a departed soul" according to Snape, not a complete soul. Now, this isn't hugely clear, but it does seem to heavily imply that broadly speaking in JKR's mind, ghost =/= soul.
"A ghost, as I trust that you are all aware by now, is the imprint of
a departed soul left upon the earth, and of course, as Potter so
wisely tells us, transparent." - Severus Snape, Half-Blood Prince
The Pottermore article on ghosts does elaborate:
No physical pleasure remains to them, and their knowledge and outlook
remains at the level it had attained during life, so that old
resentments (for instance, at having an incompletely severed neck)
continue to rankle after several centuries. For this reason, ghosts
tend to be poor company, on the whole. They are especially
disappointing on the one subject that fascinates most people: ghosts
cannot return a very sensible answer on what it is like to die,
because they have chosen an impoverished version of life instead.
Because their knowledge and outlook doesn't change over the years, I would definitely conclude that a ghost is not a soul, as canon does tend to point towards the view that your soul is your entire character and personality, evolving changes and all. (Interestingly, it's not clear what happens to the "actual" soul - it's definitely not on earth, but we don't know if it's "moved on" or not.)
In this sense, a Dementor could not perform a kiss in the traditional sense, because there's no soul to grab on to, and no body to leave behind. Arguably, though, an imprint could be enough - the Dementor may be able to "suck away" the imprint of the soul (the ghost) and leave nothing behind. As far as I know, there's no canon explanation for this, but it seems plausible.
As to whether a ghost would be affected by the nearby presence of Dementors as humans are, forcing them to remember their worst memories - I'm not sure, but I suspect they'd be affected in a similar, if not identical way, to humans. Given that they still have their memories, and clearly can be influenced by the outside world to an extend (e.g. Nick and the Basilisk), I would find it odd if the Dementors were busy chilling everyone nearby while Nearly Headless Nick and the Fat Friar had a singsong. (There may be a clue about this when the Dementors are in the school in Prisoner of Azkaban - I'll look into it more and update later.)
To answer your last point - could a rogue ghost be imprisoned? I don't believe so.
"Wizards can leave an imprint of themselves upon the earth, to walk
palely where their living selves once trod" - Nearly Headless Nick,
Order of the Phoenix
"And then, of course, she went to the Ministry of Magic to stop me
stalking her, so I had to come back here and live in my toilet."
Moaning Myrtle on Olive Hornby, Goblet of Fire
This, to me, suggests that ghosts can only walk where their bodily selves went when alive. This explains why so many of them end up at Hogwarts - they all attended it as students, and it's a place where they can all hang out together. Following that logic, most ghosts couldn't end up in Azkaban (unless they'd been imprisoned there during their lifetime). Not to mention the fact that walls or islands would not contain beings who can easily travel through walls. So, I think the Ministry would have a different way of dealing with such ghosts (although sucking their entire remains away would seem a little harsh).
It's also unclear how much damage a rogue ghost could actually do - they can't really affect the physical world around them to any great degree, and they're unlikely to start a riot, since as Pottermore notes, they're not very good company. It seems as though those who would choose to remain ghosts are not inspiring leaders either - there are several ghosts we meet throughout the series, but I can't imagine any of them leading an uprising.
