"We are listening to you."
Translation:Nous vous écoutons.
Tu (the subject) never contracts, but te (as a direct or an indirect object) must contract when it comes before a vowel. In your first example, tu écoutes — you (subject) are listening. The second example is incomplete, but t'écoute means something or someone is listening to you, you (object) are being listened to.
Je t'écoute. — I am listening to you.
Elle t'écoute. — She is listening to you.
Ils t'écoutent. — They are listening to you.
I'm not Sitesurf, but I can tell you that that doesn't work in French. First of all "écouter" like "chercher" does not require a preposition in French, unlike English.
On écoute les oiseaux. → We are listening to the birds.
Je cherche mon sac. → I am looking for my bag.
Secondly, when you have a direct object pronoun, it precedes the verb. A pronoun, of course, replaces a noun. The direct object pronouns are me, m', te, t', le, la, l', nous, vous, les.
Nous les écoutons. → We are listening to them.
Je te cherche. → I am looking for you.