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A quote: "The mission plans to use a modified SpaceX Dragon capsule with an inflatable living module attached. It will be mostly carried by gravity [sic] on its way to Mars and back home"

A spacecraft on an unpowered trajectory between two planets is not "carried by gravity", it proceeds by way of its own inertial momentum -- energy it's been given by the launch and route insertion process.

A quote: "... the difficulties of a Spartan and low-gravity ship environment ..."

Not low gravity, but essentially no gravity or microgravity -- only the gravitation of the spacecraft for its occupants and vice versa.

A quote: "... as a ‘free return’ trajectory. The same approach was used for NASA’s Apollo missions to the Moon."

False. The Apollo craft had to be inserted into, and removed from, lunar orbit by rocket burns, then the separated lunar landing craft required two additional burns to get down to, and back from, the surface. Even the ill-fated Apollo 13 mission required a correcting burn on the moon's far side to get on course back to Earth.