If done properly you could technically have the LRTs run with buses like in a mixed-traffic situation, albeit just with transit vehicles.
It would mean that the system could not be driverless however.
That being said, the LRT would replace a lot of the buses that go the whole route of the Transitway. You wouldnt be pushing those buses back onto the 403... they simply wouldnt exist anymore.
A GO/city bus from the west would just terminate at Winston Churchill and youd transfer to the LRT.
Yup, there's nothing stopping LRT tracks from being laid in a road. Buses run overtop of streetcar tracks in Toronto all the time. At stations, the tracks would pull into the right lane to allow the trains to service the station, while the bypass lane would be a bus lane only. That's only if you need to maintain through bus service though.
Your 2nd point is also quite valid. The configuration I envision is LRT east of Square One, and BRT west of it. Bus service from the western half of Mississauga and Halton Region (and potentially further afield if you're talking about GO) would all terminate at Square One. Build a proper transfer facility there, where people can make that bus <-> rail transfer easily.