With the knowledge that space exploration is open to all, can a feasible and convenient attachment site be claimed and used only by a single country?
For the time being, the status of regions of interest on celestial bodies remains res nullius. I.e. there is no ownership rights, no state can claim exclusive access or otherwise prohibit other states, or state regulated parties from exploring such regions. This was drafted in the resolution of the United Nations General Assembly in Declaration of Legal Principles Governing the Activities of States in the Exploration and Use of Outer Space more commonly known as The Outer Space Treaty (OST), ratified and signed by most countries.
Namely, governing principles that carry the most weight with regard to your question are:
- Outer space and celestial bodies are free for exploration and use by all States on a basis of equality and in accordance with international law.
- Outer space and celestial bodies are not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.
As you can see, these two principles can oppose each other, and so far not much has been done to amend this, so is subject to open interpretation. This is not ideal, but while OST was also the basis for other space law treaties, among which Agreement Governing the Activities of States on the Moon and Other Celestial Bodies aka The Moon Treaty that remains mostly unratified, unsigned by most countries and is considered a failed agreement that was seeking to increase international cooperation (including e.g. sharing samples) and to reaffirm common heritage status of celestial bodies.
Through other treaties and agreements (e.g. Convention on International Liability for Damage Caused by Space Objects, aka The Liability Convention and Agreement on the Rescue of Astronauts, the Return of Astronauts and the Return of Objects Launched into Outer Space, aka The Rescue Agreement) obligation of individual state parties to OST was emphasized and with it their legal reach. Some countries, including e.g. US, are trying to take this opportunity to draft unilateral laws that would regulate exploitation of outer space resources as they deem fit, as long as they broadly follow OST convention.
One such try, or at least one of the latest ones, is the ASTEROIDS act of 2014 that the US House of Representatives had on their agenda, seeking to protect property rights and establish a legal framework for commercial exploitation of outer space resources, but so far didn't pass for being in need of more work.
So in short, no. For the time being, there is no wherewithal legal framework upon which any signing / ratifying state party to the OST could claim ownership or exclusive access rights to any celestial bodies, or their individual regions of interest. So caveat emptor when someone tries to sell you a deed to a property on the Moon, or on any other celestial body!
There is a glaring loophole in all of this tho. Since, by massively ratified frameworks like The Liability Convention, launching countries bear responsibility for space objects that are launched within their territory, that also means the spacecraft and any supporting infrastructure they use are effectively that launching state's territory. Combined with non-interference provisions of OST, this creates an interesting (for lack of a better word) stage for exclusive access by means of occupation. So if you can attach to any of these regions of interest and stay attached, you're effectively prohibiting others access and via non-interference they can't access it without your consent. You're supposed to enable them access, if so requested, but only under your terms which aren't internationally provisioned. A form of outer space squatting, if you want.