"We can do it."
Translation:Noi ce la facciamo.
"Farcela" is idiomatic, it means something along the lines of "make it", "overcome the obstacle". Your boss handing you an assignment might ask you "ce la fai per stasera?" (can you do it for tonight?) meaning "do you think you can make it within the day?"; "puoi farlo per stasera?" instead implies you can make it, and asks whether you accept to do it.
Digression aside, "Possiamo farlo", "Possiamo farcela" and so on are all acceptable translations.
Hmm... I don't know xD Among the options the dictionary gives I'd probably pick the indeterminate locution as in "ci vuole" (it's needed), but I can't figure it out. Browsing through the grammar sites it seems it's called a "verbo pronominale" and conjugated together with the pronouns (ci and la); this site (in Italian) lists some of them with their meaning and an example of conjugation: http://www.zanichellibenvenuti.it/wordpress/?p=3308
"ce noi lo facciamo" would be wrong, all clitics must precede the verb in the present.
"Ce" is there just to change the meaning into an idiomatic one, and in that meaning the direct clitic is always feminine:
- noi lo facciamo: we do it, we make it
- noi ce la facciamo: we can do it, we can make it, we're not going to miss the deadline, we'll overcome the difficulties.
- la faccio da solo: I do it, I make it on my own
- ce la faccio da solo: I don't need any assistance, I'm doing fine on my own.