If something hinders you, it keeps you from moving forward. It's usually an outside obstruction. If something hampers you, then it prevents you from doing something freely. The problem is inherent, or at least immediate (eg. wet clothes which hamper a swimmer).

Hamper is less colloquial. It is used less often than "hinder". But they have the same connotation. You may say either "hamper movements" or "hinder movements", no difference.

Pretty much the same in most cases, however you can use hindrance as a noun for something that hinders

In a medical context, if,say, a patient behaves in their daily life in a way that prevents them from completely recovering from a disease or a health problem in general would you say that their behaviour is hampering OR hindering their way to recovery?

obviously I meant *CAN'T figure it out. sorry for the mistake.