Learn Italian: Sei proprio gentile.

In Italian, the subject pronoun tu (you) is usually left out because the verb form sei already tells us exactly who the subject is. You would only add tu before it if you wanted to add special emphasis, like saying 'YOU are really kind.'

Does gentile change if I am speaking to a man versus a woman?

No, it stays exactly the same! While many Italian adjectives end in -o for masculine and -a for feminine, adjectives that end in -e in their singular dictionary form, like gentile, are used for both masculine and feminine.

Could I use molto instead of proprio to say 'really' kind?

Yes, you definitely can! Sei molto gentile is very common and means 'You are very kind.' Using proprio is just another natural way to say 'really' or 'truly' to emphasize a compliment.

Does proprio change its ending depending on who I am talking to?

No, because here it acts as an adverb (a word that modifies an adjective) meaning 'really.' It doesn't change its ending to match the person you are talking to, so it always stays proprio in this context.