Of course you can. That’s the point of advance parole.

Yes, you can. I know one guy who traveled to Canada on advanced parole to land as a Canadian PR and then returned to the US. But you will need a Canadian visa. Also, if you are flying from Canada to the US using one of their major airports, you will go through customs at US preclearance facilities in Canada. That means you won't have to go through customs once you arrive in the US.

Yes you can! i have travelled twice on Ap to Canada. You do need a visitor visa though