Yes, Starship needs legs to land on the Moon or Mars. They will be lighter than legs for Earth landings, as Moon/Mars have lower gravity.
Not sure about the amount of fuel needed to land, as there is much less atmosphere on Mars, and none on the Moon. I would still guess that it needs less fuel there as well.
Not sure about the amount of fuel needed to land, as there is much less atmosphere on Mars, and none on the Moon. I would still guess that it needs less fuel there as well.