Let's assume that I have all the resources to be able to travel to Mars or any other celestial body and colonize it. It is legal to colonize celestials bodies in space?
I think I read once that by international law, no country can colonize space. Is this true? If it is, will it apply to me as citizen of United States?
The main treaty here is the Outer Space Treaty and its implementation in US law. For your purposes, the relevant sections of the treaty are Article II:
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.
Article VI:
States Parties to the Treaty shall bear international responsibility for national activities in outer space, including the Moon and other celestial bodies, whether such activities are carried on by governmental agencies or by non-governmental entities...The activities of non-governmental entities in outer space, including the Moon and other celestial bodies, shall require authorization and continuing supervision by the appropriate State Party to the Treaty...
and Article VIII:
A State Party to the Treaty on whose registry an object launched into outer space is carried shall retain jurisdiction and control over such an object, and over any personnel thereof...
Article II means that setting up your colony doesn't give you ownership over the land it sits on (and Article XII permits anyone to stop by for a visit at any time), but it doesn't outlaw setting up a permanent base.
And I hope your "all the resources" includes a small army of lawyers. Between them, Article VI and Article VIII make the United States government responsible for anything you do in space, so there's a lot of paperwork involved in getting permission to do anything above the Karman line.
I don't think it's entirely regulated yet.
The Article II of the Outer Space Treaty states that "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." And the article VII says that the only ownership that a state can have is on the artifacts used to get there or constructed there.
In theory, you can build your personal dome on Mars and live there, but you can't appropiate a single molecule, so extracting water or stone for personal use could be legally troublesome.
There is, however, the Commercial Space Launch Competitiveness Act of 2015 (complete text here), that allows US citizens to "engage in the commercial exploration and exploitation of 'space resources'". This may be a US' step toward colonization, but it obviously violates the Outer Space Treaty, and both may be overriden soon by a future act, written to suit corporative interests rather than political ones, judging by the commercial twist space exploration is taking.
This is my interpretation of Space law based on conversations with people who have studied space law, law of the sea, property law, international law, and contract law in a number of countries and my own research.
The Outer Space Treaty is the main basis, and it requires a treaty state to be responsible for the actions of any non-government or other entity.
So assuming you offered to compensate or benefit "Everyone" fair value for what you used and some rent for the space you occupied, and you did so compliant to USA law the answer is you could go to Mars, or anywhere else extra-planetary construct what ever was necessary to function as a productive USA citizen, pay taxes and expect reasonable support from the Federal Government. Eventually a sufficiently large number of people would be able to apply for state hood.
If you choose to exercise your right to terminate your citizenship, then you need to join another sovereign treaty nation or be recognized as a sovereign nation and sign the treaty.
To pay to "Everyone" you would probably be covered if you paid some "reasonable" amount into a trust used for general benefit. I would suggest 10% of costs would be sufficient.
I am not a Judge (potentially able to set precedent) or even a lawyer.
I am involved in a project to simulate 1 billion plus people living in space.
