Usually you can modify everything inside the condo (walls, floors, ceilings) as long as it doesn't compromise the structure of the building. In smaller condos (4-6 units) sometimes you can change the siding of the outside or the roof of your part too, depends on the building.

A house isn't so different in that there are restrictions, since you have zoning codes and stuff. It's ownership in that you own the right to live inside it and sell it and modify it within reason.

I guess, kinda, but the concept of "ownership" isn't the divine right of kings. It's an understanding of possession in relation to the rest of the world and other people. There are like zoning laws and shit like that for a reason, just because you buy a piece of land doesn't mean you can develop it into whatever you want and put a chemical processing plant in a residential neighborhood.
Just because you bought an apartment and maintain exclusive ownership of it, it's in the context of someone else owning the building, and someone/thing further owning the area that building is in. Ownership doesn't give you any right to alter something in a way that affects the other peoples owned property or possessions.
Not that I'm advocating that it's right or even a good thing, but essentially the "final boss" of ownership is the government because people can't be trusted not to be petty dicks to each other