I'll let someone else chime in on the specifics of your regs related questions. What I will tell you is my experience of how VFR On Top works in the real world situations I've used it in.

I've never tried it on a flight to another airport (which seems to be what a lot of your questions are related to). I just file IFR and be done with it. What I use VFR on top for is getting out to the practice area when we have low ceilings and low tops.

I file an IFR flightplan, with "VFR On Top" in the remarks and let clearance know that when I call up. Every time I've done this, the student climbs out, we report when on-top, and approach lets us do whatever we want to, while keeping our IFR code. I've offered to cancel IFR, but they have always told me it's not necessary (usually with an instruction to remain above a certain altitude).