Adult living at home: What are my rights?

IANAL etc.

Yes, because his legal status changes from “member of household” to “tenant.”

My admittedly limited understanding of the case law is that no, it is not, because the nosy neighbors are not the police or agents of the police.

That you would even ask this as a question indicates your youth. Trying to stand on legal search and seizure code regs as a non-rent paying 18 year old living in your parents home is absurd in a real world, practical sense. Your history with them is going to govern whether they stay out of your room or not, not the threat of legal action and/or whether you are paying them rent or not. If you came back to their house after being away as an adult the expectation of privacy context would be different, but as it stands you’re still just their kid and they might well toss your room if they suspected you were doing bad stuff.

If you want real privacy move out. If you need privacy because you may be induging in herb occasionally or holding your stash there please move out. Depending on the nature of the drug laws in your state your parents may wind up fighting not to lose their house if a sufficient quantity of drugs is found on premises.