Space tourism;
Not prohibited, but limited in terms of locations. While the only accessible tourist object is the ISS.
For all the time of existence of the station, seven non-cosmonauts visited it. Among them, Hungarian billionaire Charles Simonyi, developer of games Ultima and Lineage Richard Garriott, as well as the creator of Cirque du Soleil Guy Laliberte. British singer Sarah Brightman, who planned a tourist flight to space in 2015, as you know, eventually refused it, referring to family circumstances.
However, recently there was information that in September 2017 the eighth space tourist could leave for the ISS, which, perhaps, will even make an exit into outer space. But nothing is known about the identity of the candidate.
Plans for the colonization of other planets;
In this formulation, they are illegal.
Since, according to article II, "outer space, including the moon and other celestial bodies, is not subject to national appropriation, either by proclaiming sovereignty thereon, or by use or occupation, or by any other means."
Therefore, the first expeditions to Mars will not give any territorial advantages to countries whose astronauts will be included in the composition of the crews.
However, in the near future such flights are not expected. The estimated date of the first manned flight to Mars is 2030.