1. It needs to be operated and marketed BA nothing else on the PNR. There are some work arounds for short legs.
2. Yes as long as the ticket can be priced, BA flights on BA stock.
3. I have found propeller to be excellent. The other method I find works is a small high street travel agent that is happy to be walked through the process if you make it easy for them. I have found other larger ones just do not have the time to listen or read that they can do it, and it is not like a post ticketing points upgrade. I have even had some large travel agents deliberately messing it up so I would not ask again. (Looking at you Amex).
KF