Land like this on Mars is of no intrinsic value to humans, you can't grow crops there, or plant trees. Actually myself, I think there is a reasonable chance that we won't want to have humans on Mars because I expect we'll find interestingly different life there and want to do biologically reversible exploration.
But whether or not we have humans on Mars, we might have greenhouses there that export crops to orbit - as some forms of hydroponics are possible without introducing Earth microbes to Mars. If so you'd own the greenhouses on Mars but not the land they are built on. The land is of no value anyway until you build the greenhouse on it.
Build a habitat like this - in this case a Stanford Torus - and you would own it under the OST. To avoid the solar system becoming filled up with regions nobody can use because of ancient scrap from previous failed attempts - could add agreements on top of that that if it is abandoned for some period of time then others can take it over - say after a decade, with no habitation, or where appropriate (roving machines) no remote control from Earth or elsewhere
But if continually inhabited then others would not be permitted to move it - or build another habitat right next to it - or indeed, to enter it either, without permission of the inhabitants.
Surprisingly perhaps you could build this whole habitat, for 10,000 people, from the material in a small NEO a few hundred meters across.
Mars's moon Deimos has enough material in it to build Stanford toruses with total surface area twice the size of Switzerland or same area as the state of Oregon - and that's just the ground floor of the habitats.
This is a "for instance" - whether we should dismantle Deimos in its entirety to make habitats is another matter - but whether or not - Deimos is a tiny Moon - serves to show that there is plenty of material in NEOs or the asteroid belt - which would also be easy to transport to Mars orbits in any future with extensive space settlement, if that's what we decide to do. Asteroid belt has enough material for space settlements with total land area of a thousand times that of Earth - which could be built almost anywhere in the solar system - there are techniques that would make it easy to move this material to anywhere we need it, with almost no expenditure of fuel (and get the fuel from the asteroids anyway) with enough advance notice for your order.
If you abandon your base, say for a decade or whatever, nobody living there, not controlling it via radio or anything - then others would be able to take it over.
See Mars Pathfinder
If there is interesting life on Mars we may need to sterilize all our rovers there from early missions - in this case Sojourner, quite possibly also remove them from Mars. If that's not necessary, then they may be preserved as of historical interest in Mars parks.
Destruction of ISS in Gravity. Any habitat in space would be vulnerable to destruction by an incoming spaceship or even a large piece of debris from it. So space wars in space in conventional sense would seem to be impossible - they would end quickly with all habitats of all those involved in the war destroyed.
This is equally true for colonies in space or on planetary surfaces, or the Moon or asteroids - and even colonies floating in the upper Venusian atmosphere - though protected to some extent by the thick Venus atmosphere - and not so vulnerable as most space colonies to small fast moving objects which would burn up in the atmosphere - and small meteorites anyway would just puncture the habitats - still would obviously be very vulnerable to any major collisions e.g. with an incoming spaceship.