Finding a rental in Napa, CA (wine country) for that price point would be really hard to find. If you don't mind the commute you should be able to find a few in Fairfield, CA that match your requirements.
Very unlikely. I have a 3/3 rental in Napa and I charge 2400. I could probably get more, but I hope to keep my tenant in the house for many years. If you do find something in that price range I would be surprised, and most likely in a questionable area of town.
We have been looking for a 3 bedroom place with even just 1 bathroom (pref. 2) and have found 3 bed/ 1 bath for between $1650-$2000. We have also found 3/2 apartments or townhouses from $1900-$2350. Anything we have come across as 3/2 have been between $1900-$3000. You pay to live in tourist country when you choose to move to Napa, CA. Happy house hunting.