I lived in Palo Alto in a 2BR/2BA apartment near El Camino and California. Not the most luxurious space, but it did me just fine. I was alone, so I Airbnb'd the 2nd room, earning about $2k a month. My rent was $2700, plus ~$100 for utilities and Internet. I made enough that the $2700 wasn't a big deal if I had to eat the whole thing, but I was alone, so I optimized. MPK's free food definitely helped me keep costs low too, but of course, that doesn't quite help the rest of your family.
These are questions best answered by Peeps @ FB, but you're not the first, and I'm sure they have plenty of resources to help you out.
All said and done, it's definitely doable, but depending on your salary, it could be tight. If you want a bigger/cheaper place, consider MV, Cupertino, or Redwood City, or even San Jose. Heck, Oakland's a great option too. Check the shuttle schedules to see what works.
I enjoyed my time there, I'm sure you will too. But ultimately, you have to answer this for yourself!
Your recruiter can do the same thing, of course.
My personal advice:
You control how much time you spend at work and doing work at home. I've gone through periods of being very careful of not doing more than ~40 hours a week of work, and also taking advantage of the ability to work from home some of the time. I've also gone through periods of doing much more than that, because I chose to. I am confident I would not be looked upon differently not having done so.
When you choose your team after Bootcamp, make sure you are clear with your manager on how you want to work. (Feel free to reach out to me after you start - my unixname is nbm.)
Don't worry about having to keep up with young single, hang-out after work crowd. You'll likely come in earlier, focus better, and bang-out the work quicker. The older managers will appreciate family is a priority.