This is (probably; we don't know what's been going on in High Rock for the last two centuries) true in modern High Rock, but keep in mind that before the Warp of the West, High Rock harbored too many kingdoms to count, and keep in mind that, given the Bretonnic love for hierarchy, I wouldn't be at all surprised to find client "kingdoms" nested within larger kingdoms. So, while the five kingdoms is a good perspective to take in a broad view, it's more complicated than that.
We in the https://docs.google.com/document/d/1dM0O4dV7lMBQjqDMLfM3MIpcISy6JbaJsBOjiw8YxJI/edit?pli=1 project have been brainstorming for that region under the name Dunlain. It's fitting, in a way, to call the whole region that, given the http://pastebin.com/6yDSFhux of the http://www.uesp.net/wiki/Skyrim:Augur_of_Dunlain and the beautiful symmetry between the names http://www.uesp.net/wiki/Lore:16_Accords_of_Madness,_v._XII (another name for the Rivenspire region) and http://static2.wikia.nocookie.net/__cb20120626044012/elderscrolls/images/5/55/Dunlain_Falls.png.
But as far as we have been able to dig up, there isn't yet any 'official' name for the region.
The majority of them are in Skyrim, really. The Reach is more fundamentally a High Rock region than a Skyrim region, but the place is officially (according to the Nords and the Empire) a part of Skyrim, and we've seen it in-game.
Well, no one faction can really ever control the whole of the Iliac, but I'd say that Daggerfall, Wayrest, and Sentinel wield the most clout, as per usual.
I've heard the idea that the http://www.uesp.net/wiki/Lore:Cicero%27s_Journal_-_Volume_2 may have stuck around rather than buggering off, though. It'd be interesting to see a Corsair Kingdom or Republic of some sort based in Wayrest, ruling over the Iliac with an iron fist.
High Rock and Hammerfell have always been close cultural and political partners, at least in the Iliac region and along the Bjoulsae. There isn't really a hard line between the two countries; instead, there is a great big blur. We haven't had any word on your specific question, but considering the old ties between the two nations and the Bretonnic penchant for straying from Cyrodiilic management, I'm willing to bet that they're still getting along well.
We haven't had much word of how High Rock is doing under the Empire, but I'm assuming that the Empire only has a minor role around there. Cyrodiil is stretched far enough as it is, and High Rock isn't particularly easy to access, given than there are no certain land routes (Hammerfell is hostile, and Skyrim is not only in a state of chaos, but is cut off from Cyrod by some problems along the Pale Pass) and that any naval journeys would be either dangerous, long, or both. The Empire didn't help when corsairs were raiding Wayrest, apparently.
High Rock has always strained under Imperial rule. If the Empire collapses, they'll get along on their own well enough in all of their squabbling kingdoms.