is homonym used correctly?

If you ask me,there's no hobby like fishing

Yes. You've used all of the words correctly. :-)

Yes, the word "homonym" is used correctly in the given statement. A homonym is a word that sounds the same as another word but has a different meaning. In this case, the word "like" is a homonym because it can be interpreted as both a preposition (indicating similarity) and as a verb (indicating enjoyment or preference).