‘Is’ is more general. It would be better if you are describing the general terms of the loan which are always true. ‘will be’ sounds like you are taking about the future result of a specific loan.

I’m not a teacher so maybe there are some rules I don’t know about. But I’m a native speaker and either option sounds fine to me. Your suggestion “the loan will be paid back” sounds better and more natural in everyday speech. “The loan is paid back” sounds a bit more formal and maybe a bit more general, but it means the same thing.

I would say both are grammatically correct. The only think is when a story is told or terms and condition given it is more of a description and you don’t have to address anyone so passive in present simple is perfect. What was the context? Was it terms and conditions of a loan?

Well, I mean, you could also say "The loan will be paid back..", as far as I know both make sense, maybe the one you presented is more correct even..