Yes. Personally I wouldn't translate hauska as funny, especially when talking about people, but use instead maybe some example anonyneko mentioned there. In my opinion "hassu" would be closer to funny, though still more positive and not so much "weird in the head" -implications there. (Talking as a native Finnish speaker btw.)
From what little I understand of the language right now, yes, it's more like "ha-ha funny". "Funny/weird" would have probably been "hassu", though it's still normally a positive word.
Hauska can also mean "merry, pleasant, fun" (e.g. "matka oli hauska" - "the trip was fun/nice"), I think the exact meaning may rely a bit on context.
No, this suggests that both work as translations in some contexts, not necessarily in this particular context. The hints are not tailored individually for each sentence as far as I know. The course creation tools might not even include the functionality to tailor them for each sentence.