1: Would a woman with a large bust experiencing zero-gravity in outer space require her normal support bra? And, if not, what shape would her breasts assume?
2: Why do Martians have green skin? Or rather, how did the science-fiction tradition that Martians have green skin begin?
1: A woman does not need a bra in zero gravity. She can experience for herself the shape her breasts would assume by swimming braless. Breast tissue has an almost neutral buoyancy in water, and the shape of the breasts would be controlled by tissue elasticity. The effect of zero gravity is very nearly the same. The breasts would not weigh anything in space but they would still have mass and momentum. It would feel similar to swimming in water without clothing. If they are large breasts, then this COULD prove to be disconcerting both for you and your fellow astronauts.
The problem was considered in the 1973 science fiction novel written by Arthur C. Clarke, Rendezvous with Rama, in which he wrote: "Some women, Commander Norton had decided long ago, should not be allowed aboard ship; weightlessness did things to their breasts that were too damn distracting. It was bad enough when they were motionless; but when they started to move, and sympathetic vibrations set in, it was more than any warm-blooded male should be asked to take. He was quite sure that at least one serious space accident had been caused by acute crew distraction, after the transit of a well-upholstered lady officer through the control cabin."
2: The tradition of green Martian skin seems to have been started by Edgar Rice Burroughs in his Barsoom series, which began with A Princess of Mars in 1912 and continued over the next 30 years. In these books, the protagonist fights numerous Martians of various skin colors, one of which was indeed green. One might surmise that the color green was chosen for it's fearsome quality of being associated with slime and decay.
Prior to Burroughs, and even long afterwards, there was no tradition within written science fiction that Martians were of any specific colour. H. G. Wells, in his seminal The War of the Worlds (1898), describes the Martian skin as "oily-brown" and Edwin Lester Arnold, in his classic Lieutenant Gulliver Jones: His vacation (1905), assumes Martians to be completely human-like.
Most recent abductees report the aliens to have either gray or pale white skin. I suppose that's more believable than: "I was taken by little green men."