Sending RTK GPS data using MAVSDK MAVPROXY

You may check the mavlink message list
https://mavlink.io/en/messages/common.html#RTK_BASELINE_COORDINATE_SYSTEM
But I think you may also on the Ardupilot/Px4 forum, as this is more a software problem. Developers that can give you better understanding on how the data are being received and processed.

I am not sure how your system works, but won’t it be easier if you use ground control station to send the RTK base signal to the autopilot?

For you 2nd question, it depends on whether the firmware support it or not.
For example:
https://ardupilot.org/copter/docs/common-positioning-landing-page.html