As for the problems, we solve them like we always have: one at a time. Additionally, some of these things haven't even yet been studied to the extent necessary to take a crack at solving them. Taking the humans in microgravity problem as an example, we know it's a problem but have done precious little in figuring out things like exactly where the minimum threshold sits for gravity, whether simulated gravity via centrifugal force is adequate, etc.
I do think that SpaceX is jumping the gun a bit. I'd rather take it a touch more slowly and first do things like put a centrifugal space station in orbit to perform studies on. That said, after how crewed spaceflight beyond earth's orbit came to a screeching halt with the end of the Apollo program, it feels like a miracle to be getting anything.