You haven't told us much about the relationship between these two, but Kara clearly finds Clark's efforts to explain something very irritating.
Patronizing means talking down to someone, treating them as an intellectual or social inferior.
A tutorial is a formal lesson, often at a university.
Watermelon is clearly being used adjectivally here: Clark has used a watermelon to show Kara something in the past; maybe used it to represent her head. Some women would find that very offensive; he should have thought of another way to explain about controlling heat vision.