"We are free!"
Translation:Wir sind frei!
It is common to say: "Der Eintritt ist frei." And: Kost und Logis (board and lodging) sind frei. But otherwise it is better to say something is "kostenlos" or "gratis". You can say: "Das ist Freibier." But: "Das Bier ist frei." This sounds more like: "That beer is independend." It is better to say: "Dieses (or "das") Bier ist kostenlos."
Frei can refer to both the condition of liberty in people as well as objects being free of charge. "Ich bin frei!" (I am free) and "Der Eintritt ist frei" (The entry is free) both work. However, "kostenlos" (lit. cost-less) does not refer to liberty, it just refers to price. "Der Eintritt ist kostenlos" (The entry is free) works, but "Ich bin kostenlos" doesn't.
I also think that in some contexts "We are free (of cost)." is something that someone might say. If you were only supposed to pick the one best translation I wouldn't go with 'kostenlos', but when they ask for all possible translations it seems like it ought to be included.
They are different conjugations of the verb sein (to be). Use bist with du and sind with wir/sie/Sie. http://german.about.com/library/verbs/blverb01.htm