Learn Spanish (Latin America): Tú siempre estudias en tu cuarto.

Estudias comes from the regular verb estudiar (to study). Because the subject is tú (the informal version of you), you drop the -ar ending and add -as. If the subject was I, the verb would be estudio, and for he or she, it would be estudia.

What is the difference between Tú and tu in this sentence?

The first one, Tú (with a written accent mark), means you as the person doing the action. The second one, tu (without the accent), is a possessive word meaning your, as in tu cuarto (your room). The accent mark is the only way to tell these two identical-sounding words apart in writing!

Can I leave out the word Tú and just start the sentence with Siempre estudias?

Yes! In Spanish, you can usually drop the subject pronoun entirely. Because the verb ending -as in estudias already tells us exactly who is doing the action, the word Tú is optional. Including it here just adds a little extra emphasis.

Does cuarto always mean bedroom?

Not always! While it commonly means room or bedroom in everyday conversation, it can also mean a quarter (a fourth of something) or fourth as a number. When talking about a house, it simply refers to a room.