I'm working on creating a planet that is tidally locked to a red dwarf, which is in turn orbiting a main sequence star which is much further away. My idea is that the tidally locked side of the planet is far too hot to support life, but given that the planet is small and has a thick atmosphere, so strong winds constantly circulate between the "always bright" side and the colder day/night side. My question is: what would the temperatures and wind patterns actually look like? What would be the optimal/strategic place for a civilization to inhabit on this planet, and what would some rough distances be to ensure that the orbit of the planet around the red dwarf was stable against the perturbations from the main sequence star? Is a small planet with a significant atmosphere this close to a red dwarf even possible?
As air would be heating up on the sunny side and cooling down on the dark side of the planet, winds would probably go from dark to sunny on ground level and in the other direction higher up. You could expect them to be fairly strong and regular.
As a result of cold air being sucked from the dark side there would be a zone in the sunny side with reasonable temperatures, as the cold gas sucked in only starts to heat up when in the sunny region. That would be a good position for a colony.
The steady winds provide a source of power and the temperatures wouldn't be too far off. They would have to live underground though and be ready to repair their wind turbines as red dwarfs are quite lively and emit enormous solar flares.
For that reason a civilization might opt to settle on the dark side, still using wind to generate power and accepting the downside of extremely cold temperatures for the upside of being shielded from flares much better.
For the last question the answer is maybe. On one side, solar flares could deplete the atmosphere rather badly, on the other side there might be enough gas coming out of the sunny side of the planet to compensate as it would be so hot there.