2. How to confirm complete RX FIFO reset?
As UM mentioned, RX FIFO Reset bit is self-clean, once you set this bit, poll this bit and wait until it goes to zero.
(3) Not just UART, any FIFO reset in the middle of the data communication will cause data corruption, overflow or underflow, frame error, timeout, etc. Some basic house keeping is needed before FIFO reset can happen, for the UART case, I would check the LSR first, wait until RBR is empty; even after FIFO reset is done, make sure it's "clean" in the LSR register.