So you won't have the "option" of getting pc anywhere, it's just there if you get the Client Management Suite. It works very well - better than CC or DS Remote Control, more secure, more configurable, easier to configure, the works.
DS7 is more integrated than it was in NS6. Not even close. NS6 was a plug-in to manage the 32bit version that worked... well, that's a bit of a stretch, but it sorta worked. In CMS7, DS7 is another solution like Software Delivery. All of the functionality is in the same DB, shares features with other products, relies on some of those (i.e. task management), and is 100% managed from that console.
After DS 6.9, no more 32 bit console - probably ever.
Currently, if you upgrade to NS7, you can have both DS 7 and DS 6.9 still running, since they're completely different and separate apps. There is however, no upgrade "path". There is a tool to import images, but that's it.
However, because the two products are in fact 100% separate, yes, you could keep DS 6.9 up and running on a different box. On the same one technically, but I'd recommend against that pretty strongly.
As for your remote control issue - I've not personally heard of it and think it should be working. That said, there's no work being done on it because 1) we have remote desktop and 2) we have PCA. If you're getting errors, be sure to look them up in the KB. Pretty helpful. :D