Without cheap space access they are not even worth properly researching.
> One where all of the waste we produce can be reused to create new drinkable water, air and food, and to reliably continue to do so between Mars launch windows.
None of that is as big of an issue if you can launch often and a lot of stuff. In the limit you don't need to recycle anything and everything has multiple spares. You can also launch outside direct constraints of Hohmann transfer orbit. Again, payload limitations and time are the main reasons we use Hohmann transfer orbits.
> The second biggest is probably avoiding contamination of Mars, if we actually care about exploring one of the biggest mysteries of life - has it arisen only on Earth? Are there other modes of life possible, and what do they look like?
We will not avoid contamination. It's impossible to do. Where humans go our microbiome will follow.
I personally think we should intentionally seed all celestial bodies with life as soon as possible anyway.
If we find life in our solar system (especially life independent from Earth) we should become a lot more aggressive with space settlement, because it would make "great filter" ahead of us hypothesis a lot more likely. Settlement outside solar system should become one of humanity priorities as a matter of survival.
https://en.wikipedia.org/wiki/Great_Filter
> The third biggest challenge is human psychology and physiology
Going to Mars can be a suicide mission and you will still find people who will be willing to go.
Not a showstopper for the willing.
> Thinking about an actual colony with some prospect of perpetual habitation being in orders of magnitude more issues
First things first.