>"I think the two-month delay is necessary to comply with the launch requirements, and I think that's an important part of safety culture," said Michael Whitaker, the FAA administrator
To speed up turnaround. Musk used to talk about a goal of having turnaround times including refueling and payload loadout be similar to those of passenger aircraft - much less than a day, not the ~half a week of the Falcon 9.
The booster is not going to Mars, only the ship which will have legs for the landing. I also think they plan to catch the ship as well so there will be different versions.
Not just Mars, NASA plans to land an upper stage on the moon. I think it will need pretty large landing legs, because there is no flat surface on the moon. And gravity being lower while inertia is the same means that things topple over much more easily than on Earth.