The Martian

At no point in the movie does anyone take off from the Martian surface and escape Mars's gravity by means of the same vehicle. The MAV was only designed to reach LMO, and even the stripped down version fails to reach the required velocity.

Irrelevant. NASA does not currently believe there is any feasible way to take off from the surface of Mars to return to Earth. How many or what vessels were used is irrelevant. We can't even bring our dirt samples back from Mars yet...though there are plans in the works to manage to do that, at least. Getting humans or anything of significant mass off of the surface of Mars is a much bigger problem that there are currently no feasible solutions to. The technology simply doesn't exist yet. We don't even have the technology to safely land humans on Mars, the escape issue aside.

Info about sample returns

"Advanced entry, descent and landing techniques that reduce the G-forces on landers will also be developed for spacecraft and astronaut safety."

"Engineers and scientists around the country are working hard to develop the technologies astronauts will use to one day live and work on Mars, and safely return home from the next giant leap for humanity."

I too, repeatedly asked why the HAB wasn't buried, and eventually concluded that this must be related to the short stay and the weight required for excavation equipment. Remember that the crew spends many times more time in space than time planned on the surface.

Presumably they are shielded from extreme radiation while in space, but the HAB clearly was not shielded significantly.

Info about how astronauts are protected from radiation in space.