There is no conceivable way for a change in a human's genes to enable them to alter the laws of physics (i.e. give them their own gravitational pull).
Not needing to breathe for extended periods could be made possible with some form of extremely efficient anaerobic respiration, which provides a body with energy without requiring oxygen. Currently, there are no genes in humans which code for a choice between anaerobic or aerobic respiration; whether an organism has metabolic pathways for breathing with oxygen (aerobic) or without oxygen (anerobic) is much more complicated than an on/off switch.
However, modern gene editing technology can splice foreign DNA segments into preexisting DNA strands, and has produced things such as goats whose milk contains useful spider silk or strawberries with flounder antifreeze genes for cold resistance. Sometimes, it's done via artificially-altered viruses. It is therefore clearly possible for a virus to splice foreign DNA into an organism's genetic code in a manner causes physical changes (as opposed to simply being non-coding ["junk"] DNA which doesn't appear to do anything).
Essentially: there's absolutely no way people with their own gravitational pull are possible with anything that follows humanity's current understanding of the basic physical laws of the universe, but, conversely, I'd say it's quite likely that, even in real life, gene-altering technology will eventually enable altered people to breathe for long periods (if not indefinitely) without oxygen, and our gene-altering technology today already uses viruses on a regular basis. Big no on the gravity, medium yes on the lack of a need to breathe.
Dealing with the dangers posed to the human body by the hard vacuum, cosmic rays, and extreme temperature differences found in space, on the other hand, might be somewhat more difficult. And don't forget that even a human whose bodily processes run off of super-efficient anaerobic respiration will need to breathe oxygen eventually...