I didn't spend the time searching google to provide citations, but it is feasible to generate fuel autonomously on the Martian surface and store it for future use.
Can we launch a vehicle that will de-orbit, safely land, and then begin processing fuel using nuclear (edit: I removed solar here; solar would not provide enough power for such a facility) for power and the Martian atmosphere and soil as feedstock? Not quite yet, but we're getting there.
Side note, I'd recommend to you the book "The Martian", which just happens to involve a man stuck on Mars doing about just what you described. I had the audiobook, the narration is crazy awesome.
I don't think it is so much an issue of ability so much as desire. Most of the tech has been dreamed up for decades, but it needs funding and a green light (particularly the nuclear reactor, given that there were protests about even Curiosity's RTG).
Personally, I think there's a huge amount of talent just waiting for the right moment to strike, and then the whole Mars thing is going to burst right open.
I believe solar would work, but it would just take longer.
EDL for a substantial payload to Mars hasn't been done before, but there's no reason to think it's a show-stopper. A lot of the engineering challenges for that are the same as the engineering challenges for returning the first-stage to Earth, like supersonic retrorockets.
Can we launch a vehicle that will de-orbit, safely land, and then begin processing fuel using nuclear (edit: I removed solar here; solar would not provide enough power for such a facility) for power and the Martian atmosphere and soil as feedstock? Not quite yet, but we're getting there.