My take:
Can you make babies in space?
You probably can make them though they might be crippled due to radiation, so it's unethical. I recommend only having babies in sheltered martian habitats, where wall strength is at least 30 cm of either martian dirt or water/ice. I don't have a good source for these numbers, they're more or less made-up, i just get the vibe that would be enough for appropriate protection.
Should corporations govern space settlements?
While corporations certainly play a large role in producing the rockets and the machinery needed to live on mars, eventually ownership of the martian settlement should be with the actual settlers. It is noteworthy that it is difficult for earthian governments to enforce/regulate policy on mars, so if martian settlers decided to "steal" company equipment, it would be nearly impossible for earth companies to stop settlers from doing so.
What about space war?
Space war is a real threat and discussed in cultural media such as She-Ra. It is possible that martians eventually grow greedy and try to overtake earth, possibly because they see themselves as technologically superior. While rockets filled with explosives can do real damage, it is easy to spot them from a large distance (because rockets from mars to earth would have at least 6 months travel time) and to take action to shoot them down. So, defense in planetary war is a rather predictably possible and surprisingly easy task, i guess. Further details are needed.