As a native English speaker of 71 years I can say unequivocally that the only times I have heard 'You do that which is right' are in Hollywood movies or on stage... both usually said by mother or father figures to a sibling or by 'a man of the cloth'. To my friends, family, acquaintances, co-workers etc, I have and would always say... 'Do what's right'. I'm learning Italian to talk Italian in Italy... and be more or less understood... I will not be pontificating, moralising, being pretentious or worse, to those whom I meet.
"fai" is not the imperative form of fare so it cannot be used as a command. http://italian.about.com/library/fare/blfare160a.htm
Because (tu) "fai" is correct alternative form for imperative of the verb fare.
This sentence has two possible nuances from my experience as a native, a statement or an exhortation/a comand:
(Tu) fai quello che è giusto ogni volta che c'è un problema.
Fai/Fa' quello che è giusto! (the elision of 'fai' is not mandatory).
In the written language it is very frequent to add " ! " to avoid misinterpretations in these ambiguous cases.
No be careful guys, Craig Pickering is right:
what/that which = formal ciò che / informal quello che
So 'what' is correct here. It translates a double pronoun: neutral demonstrative pronoun + relative pronoun. The neutral pronoun ciò/quello is used speaking about undefined things and it's always invariable (no inflections for gender/number).
Speaking of definite things instead it's possible to use quello che only and not ciò che and you need to translate it with the one e.g.
Quello che ho comprato è il libro di Jim. = The one I bought is the book of Jim..
Also, in these cases quello che has the inflected forms quella che (the one), quelli che, quelle che (the ones), because we're not speaking about general things.
As for the rest, what also means che cosa/cosa/che, an interrogative pronoun/adjective.
In everyday English they'd be interchangeable, but the important thing is to nail down the tense used because it matters more when we're learning the grammar. Your first response is present continuous tense whereas the answer is just present simple (or imperative/command form if need be).