Not just mental health, but physical as well. Humans are not well suited for long term high G environments, while I have every expectation that we will someday make it to other planetary systems I doubt the meatbags will be coming along.
It's the solar radiation, not high G's, that is the main problem with colonising Mars given Mars doesn't have a functional magnetosphere. At best Martian colonists will be the modern day equivalent of Morlocks if they want to have a sustainable colony on mars.
Not if you design the habitation appropriately. Something like a 1m layer of water in the roof and thick glass windows would provide pretty decent protection.
