Yes, the F4 and F0 are significantly different parts internally, you'd need to review the DMA plumbing in the F0 and pick more appropriate channels and TIM. See the Reference Manual.
Almost certainly some level of SW UART would be achievable, though not super desirable and you are already very resource constrained. Might have to write/port yourself, so best to understand the mechanics, or pick a part with better feature-set.
