Does she have to use a full-fledged PC? Seems to me this is what tablets were made for. My 85-year-old Aunt Eldine has no problem with an iPad.
The thing about VNC is that it doesn’t do NAT tunnelling out of the box, as far as I know, and since most PCs are using NAT to connect via a router, VNC becomes a real pain to set up, because you have to configure port forwarding on the router - but I’m happy to be corrected on this. If you’re on the same LAN as the remote PC, that’s great, but across the Internet, it’s trickier.
You definitely can. In TeamViewer jargon, it’s called “unattended access”; of course, you’ll have to connect manually using the ID and password the first time round, but after that you can set it up to allow unattended access. Overview here: http://www.worldstart.com/how-to-set-up-unattended-access-on-your-computer-with-teamviewer/
I can’t recommend TeamViewer enough; it’s saved my sanity multiple times when working remotely with my parents’ computer. The only caveat on Windows 7 would be that you can see any prompts that require elevated access if UAC is enabled, so you might need someone in front of the PC to click those prompts as required. I’m not sure how that works with unattended access; never had to test that.
Not sure about the others, but LogMeIn definitely has an iOS app version too. I’ve controlled my PC with my iPhone (kind of a pain in the ass with the tiny screen, but doable in a pinch).