Having the keyboard and pen working at the same time seems odd - don't recall hearing of that before. I'm guessing here, but I think the multi-mode packages could be the issue. You could try re-installing them. They are in the Software and Utilities section of the support pages: https://download.lenovo.com/consumer/mobiles/yoga_book_halo_keyboard.zip
I think you might have to go through re-installing the multi-mode and then the keyboard packages to get that to work properly. (As I understand it, if the underlying software isn't in place and running properly the keyboard section doesn't communicate with it as it should.)
When you say your Yoga Book doesn't turn off - is it just taking a long while to do so? I find mine takes 20 secs or so to shut down which is annoying. (There is a Shutdown Service package on the support site but I've no idea of what that actually does or whether it might help.)
Personally I'm not a fan of Lenovo Paper but I've not seen it causing problems except the fact that I don't like what it does which is mostly to open the One Note launcher pop-up.
I don't think it's possble to download a Recovery environment. What I would suggest is when you do get a working system is to make a System Image. I use the option available through the Backup section in Settings (Go to Backup and Restore(Windows 7)), but others swear by Macrium Reflect. Either way, then at least if things go wrong again you can get to a properly working setup again. I also usually do one before and after each major update - rarely needed them but still worth the trouble.
The tech that the Yoga Book uses for it pen doesn't require batteries in the pen. Any pen that does is using a different technology and is not compatible with the built in system. Only pens that use EMR are likely to work with the Yoga Book Create Pad.