If I buy an iPhone from someone's else, can they still report it stolen after I've already activated it?

For example: if I buy a phone from a girl on Facebook, then go to T-Mobile and it's clean, not iCloud locked, not stolen, ready to be activated. Then I activate it. Can that person then report it? Even after it's already set up with T-Mobile as active

Yes, they can.

If it's been bought on contract and they have not made all the payments, the company the bought it from can blackist it as well, possibly some weeks later…

You need a proper proof-of-purchase and ideally proof of the original purchase date, to show that the contract is complete or it was bought outright rather than on a contract.

You also need a true, verified, geographic address and proof of identity from the seller so you can contact them in case of any problem (or pass to the police if it's a stolen phone etc.)
If they will not provide that they are not to be trusted.