the answer is yes if relocate is different from re-locate. You can relocate (change the position of) yourself to another state, while you can re-locate (find again) something that you found earlier. If that's true, then you hyphenate when you find something again.
It is not hyphenated.
Motorcycle is not hyphenated
No it's not hyphenated.
words are only hyphenated when they have a separate meaning when separated than they do when hyphenated
Yes it should be hyphenated.
No, "hardworking" is not hyphenated.
It can be. Some words can be seen both hyphenated and non-hyphenated.
No. Well above is not hyphenated.
peace of mind is not hyphenated.
No, "homework" shouldn't be hyphenated.
Yes it should be hyphenated.
No they shouldn't be hyphenated.