Here are my thoughts: (yes, i know they are worthless but you asked)
1. Does anyone have experience fishing in this lake?
No.
2. How viable is it to live off of ice fishing for the winter months?
Viable. This lake seems to have warm water fish for the most part which you could eat.
3. Can fishing be accomplished when the ice is too thin to walk on?
Yes, if you are Moses or Jesus. Seriously, You'll need to keep an area open and save other areas so it freezes up, you can walk on it once it is thick enough, but until then, i would keep an area open to fish out of.
4. From my understanding the deepest part of the lake is only about 8 feet. How does this affect things?
You basically have a bait pond. Trap the rainbow smelt, suckers and shiners for bait and then go fish another lake. Build yourself a dock and put a bait box in it to hold your rainbow smelt, suckers and shiners. I'm a trout fisherman so this lake really holds nothing for me other than bait.
Good luck and let us know how you survived. Should make for some good stories and lessons.