Are RV's allowed overnight in Safety Rest areas in Virginia?

I believe so

Yes

Yes you can.

Not allowed in the semi truck parking areas

Depends on which one. The bigger rest areas near the States borders, yes. Smaller ones, probably not. I've slept over night at VA rest areas, albeit in a minivan but I've seen RVs and semi's as well.

Q. Can I park overnight or use the rest area as a park and ride location? No, overnight parking is not allowed and unattended vehicles will be towed at the owner’s expense.

I have seen them there late at night so i would say yes