What laws will be applied on Mars?
The answer is simple, space law, but, what is space law? Space law is an agreement by all countries, space law includes things like space exploration, weapons ownership/use, rescues, environmental preservation on celestial bodies, technologies, ethics, and information. Other laws, such as administrative, intellectual property, insurance, environmental, criminal , and commercial law, also figure in space law.
Can Governments claim land on Mars?
Article II states, “Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.” Which in other words means, that even if you reach Mars, there is no way for you to claim any piece of land or resources, but neither will any government or company. The equivalent of it on Earth, would be International waters, which is all the ocean or sea outside the territorial seas; which is all the sea within 22.2 km (12 nautical miles) from the coast.
The use of resources on Mars is very limited, since only the scientific exploration groups are allowed to extract and analyse. Governmental and Independent companies are not allowed to extract or mine resources yet, laws on Mars and space are constantly adapting, and I personally believe that they should change if and when we establish colonies on Mars or any other celestial bodies.
Who would prosecute space crimes?
A criminal in space would generally get applied the law of the country where they are citizen to, or the country whose registered spacecraft the crime was committed, because the treaty grants that country authority “over any personnel”. However, the term “personnel” is not defined, and this raises questions as to what the case might be for private citizens such as, for example, a Spanish space tourist flying aboard a UK-registered spacecraft.