The laws surrounding space can be pretty vague. They are almost similar to laws surrounding the internet, but the main difference is in cases where we do not have new laws to deal with the internet, we have old ones to fall back on, such as copyright laws. Space law only happened 60 years ago, and nothing else really applies in space. It is important to note the time frame and setting in which these laws were conceived. It started in 1957, with the first treaty being created in 1967, and the most recent one in 1979. Laws regarding ownership of objects in space and the use of weapons in space are all based around the Cold War.
There is some debate over what the laws actually mean. Ownership laws, for example, basically state that everything in space belongs to everybody on Earth. In 1967, that probably meant that no country could claim ownership of the moon. While this is not a bad idea, it doesn't really deal with the more modern possibility of a company deciding they want to mine an asteroid. Some space lawyers - yes, they exist - have argued that the broad definition of the law should also mean that asteroid mining and similar activities are illegal.
If in 20-30 years Google decided that it wanted to use some of their ad shekels to mine some rare space elements, would they be held accountable by international law as nations are under the space treaties, or would it be a domestic issue? In the US, there is a law that gives a framework for conditions under which companies can become subjects of international law, but that law came into effect in 1949, and really does not apply to this possibility.
With more and more private companies starting to invest in space, and seemingly less and less interest from countries, we could be dealing with this issue fairly soon.
Edit: I also forgot to mention that conventional weapons are legal in space. Laws regarding weapons in space only involve nuclear weapons. Companies could send security up into space with guns. If they shot someone, it would probably be legal, because there is no law that prevents it from happening in space.
I can't speak about the property laws or anything like that in any detail - I bet certain companies would be issues permits by national governments to claim certain bits of space junk if they wanted it or something like that - I did want to point out one thing.
Do conventional firearms work in space? I'm not a gun person, but I don't think you could get the combustion required for a gun to work without oxygen. I guess if multiple ships were docked together or something and the crews met, like on the ISS, that's another matter. The only conventional weapons I could see that would work in space would be muscle-powered ones, but those seem extremely difficult to use at best in an EVA situation.
EDIT 2: Nevermind.