1.How hard is it really to live there during the winter, or is the snowbird thing really where it's at?
Winter wasn't all that bad. I live in Palmer for reference. Honestly was prepared for it to be miserable but it was really not that big a deal. If you live closer to Fairbanks it's a whole different beast. Anchorage, Matsu, and Kenai winters are rather mild compared to Fairbanks and manageable.
2. Is the Rabbit Creek area as nice as it looks on paper? Eagle River also looks nice but a bit further afield.
Eagle River is nice but pricey. I would avoid anywhere in the Anchorage Municipality to be honest- that includes Eagle River. Politically the Muni is super disfuctional and the property taxes high. No sales tax though.
3. Any other areas to consider if I'm doing a snowbird or AirBNB type thing?
Lot of people in my ward have second homes they rent out but they don't get any business in the winter. All the tourist stuff shuts down end of August/September. The Iditarod brings some people in but not a ton. I can't tell if your planning to be here in the winter so that might not be helpful info.
4. Anyone tried doing an AirBNB in the Anchorage area (another reason Rabbit Creek is maybe > Eagle River).
See above. Kenai would be a great spot for an AirBnb. Anchorage and ER are central but not ideally situated for a lot of tourist stuff (long drives in all directions).
5. Would leaving a home vacant for a few monta hs of winter just be a non-starter (risks of damage due to poor winterizing, freezing, etc.)?
If you winterize and get a smart thermostat you can change from your phone you should be fine. Hire a caretaker service to check-in now and then.