Propellant transfer, with cryogenic propellants, can be done using cryocoolers. It's not too hard of a problem. Besides, Starship only needs prop transfer for Moon and Mars missions, but the later are fantasy and the former probably isn't going to happen either, and actually just regular LEO launches with a fully reusable rocket is where most of the money is anyway.

The heat shield is a huge problem though. Without the heat shield, there's simply no way SpaceX can use Starship to make money.