It seems to me that CBGA is easier to sold
How so, unless you have vias under each ball and to a "plug solder" from the rear.
Really I would forget about the BGA, even if you can solder it how will you design a PCB to get all those pins out unless to go to several layers. Maybe if the socket you've found breaks out the pins, but then it will be huge.
Question: is it possible to upload the Arduino bootloader and also our own Arduino code only using STK-600 + STK600 TQFP-100 adapter + ATMega1280? That is, without involving the Arduino Mega board?
I think so, but if you can do that why not just flash a chip on your PCB using ISP?