Lets says someone purchases a domain name such as www.Google.photography. This is not a generic top-level domain (.photography). If say I intend to use this site non-commercially to allow users to share photography and specify that this site is not affiliated in any way with Google Inc, is this legal practice? Could Google demand I remove this and if so would they win this? What if I am not a US citizen? What if after I bought it I offered to sell the domain to Google in case they wanted it before I started any development? Of course, I do not hold anyone accountable for any answers, this is just a hypothetical question.
I will respond to your general hypothetical. You ask numerous questions and variations which I will not address.
In practice, Google would send you a demand letter, and then you would look into the cost of defending a lawsuit and would shut down the domain. Whether their letter explicitly threatens a lawsuit depends on the particular philosophy of their trademark attorney--sometimes Trademark demand letters do not mention litigation because they prefer to be the ones filing the lawsuit, rather than having you file one preemptively.
The vast majority of cases are resolved by the demand letter. Occasionally someone has to file a lawsuit.
Note that this is under Trademark law. There is also an anti-cybersquatting law (ACPA) that can form the basis for a lawsuit, or you may find yourself in an ICANN dispute resolution proceeding. https://en.wikipedia.org/wiki/Anticybersquatting_Consumer_Protection_Act