I'm sorry that I don't know Spanish, but have prior knowledge of familiar languages. In the other languages they were used as you informal. In French and Italian both use the pronoun " tu". Italian uses ti as a direct object, for example: Ti amo. I love you. So by my experience French and Italian, I guess that all three words mean" you".
yes ,It refere to second person of singular . Tú is used like subject. Te direct or indirect object. And ti is used after a preposition. exemple: Tú eres bueno. You are good. Ella te quiere. She loves you. Juan pregunta por ti. Juan ask for you. See you.