Kayla,
Cap-10 was pretty much on, but I'll add my 0.02, having been there (albeit a decade ago). Bottom line, he needs to talk to somebody smart at the FSS/MPF and/or Airman and Family Readiness Center to make sure non-command sponsorship isn't an issue - and whatever he is told, get it in writing.
1) Yes. If his son is on his orders, his entitlements are paid out as such.
2) This might be the iffy area. Unlike Korea - where it is fairly standard to have non-command sponsored dependents - they aren't accustomed to dealing with non-command sponsored dependents. You would normally inprocess the family and provide their medical records, so I think (as Rainman said) he would probably run into some issues here.
3) Yes. There is nothing required to enter base facilities other than an ID card. That being said, she might potentially face problems in the MPF/FSS if she ever tried to renew her ID card.
4) Entire house, though you are given extra weight based on dependents.