Lambie's answer has lots of nice cultural touches. I will focus here on providing feedback for your first proposal. Good! But notice that cerrar ends in -ar, so with tú your choices are
(a) ask a question, for added politeness, and this is the indicative:
¿Cierras la ventana, por favor?
(b) use the imperative, i.e. give an order, and this is conjugated as follows:
Cierra la ventana, por favor.
(c) use the subjunctive (a bit more unusual, but valid):
Que cierres la ventana.
Notice that for the subjunctive, you have to include "que."
My focus in this post is to write something clear and simple about the conjugation of the verb, so that you will understand the various possible corrections that you could make to your sentence, which had a small but important mistake ("To my friend: cierres la ventana?"). To learn more about the myriad uses of the subjunctive, I suggest that you take a look at the existing Q&A pages on that topic, and then ask about anything that's not yet clear. The only reason I included it in my list was that you used "cierres" in your post, and I wanted to make sure you are aware that it's not wrong, it just wasn't used correctly, and with a small correction, it will be fine. (However, it is rather unusual in this context, and I wouldn't actually suggest that you use that as your jumping off place to start learning about the subjunctive.)