1. Can I use Lightroom CC, with my CS6 programs?
Yes, you can. Lightroom provides for editing in Photoshop and another external editor defined by you in the preferences. Lightroom should detect the latest version of Photoshop you have and use it as the primary external editor. I've noticed that whenever I update Photoshop CC, Lightroom uses the newer version automatically. If Photoshop CS6 wasn't detected or a newer version was set as the primary editor, you can manually set the additional external editor to be any external photo editor you have installed including Photoshop CS6.
2. Also, I mentioned on other threads that I had major trouble with Premiere Pro CS6, to the point where I won't even try using it now. I would appreciate hearing comments as to whether the Pro in CC is better, improved, less buggy than the CS6 version?
Premiere Pro CC has some great
new features. But, I can't say whether it will be more stable on your system. You'll need to try it to see. You can install it along side your older versions without conflicts. Personally, I never had any problems with Premiere Pro CS6 and have found it to be very stable. I have no idea why your experience has been different.
3. Is the video component of Photoshop CC, improved - and how - from the video in CS6 photoshop?
Video hasn't changed much. Mainly a few extra formats supported. But, Photoshop CC has a lot of new useful features and improvements. I especially like the ability to use Adobe Camera Raw as a filter. I still have both Photoshop CS6 and Photoshop CC 2014 installed, but I don't use Photoshop CS6 any more.