I believe fait means make or has, but on many of the questions where without context you can't really know which it is, it marks it wrong when I say has. So is this generally makes or is there a better word for has or should it also accept my answer?
"Faire" is a highly contextual word and "to make" is one of its basic meanings. "To have" is also correct regarding illnesses, e.g. "faire de la fièvre" - "to have a fever". It can also refer to activities, e.g. "faire du piano" - "to play the piano". And there are many other examples. Consequently, we have to learn its meaning according to its context.
The most 'primitive' translation of "faire" is "to do", which explains why it is so highly contextual. Translating sentences with "faire" will often result in "make", sometimes "have", but sometimes it will disappear while converting a noun into a verb (e.g. "il me fait peur" = "he frightens me" = "he makes me afraid")