In this sentence them is implied: in fact it would be "(voi=you) volete che (loro=them) diventino famosi? I hope it's clear!
Yes it is. Remember in Italian you have to conjugate verbs and nearly each form is different. In this case we have the verbs "volere" and "diventare" in different tenses. In particular "diventare" in this case would be:
che (io) diventi// che (tu) diventi// che (egli) diventi// che (noi) diventiamo// che (voi) diventiate// che (essi) diventino
As you can see only the singular ones are the same and this is because of the verb tense. According to this so Italians often implied the subject because it would be only repetitive and/or unnecessary.
I hope it's clear, if you have other doubts just ask! Good Learning :D!
Subj Interpretation : (do) you want that they become evolves into "to become" Point lady made of when subj uses "will"
If you look above at the response from Whitequeen17 che (essi) diventino is the verb conjugation presente congiuntivo form of diventare. che loro diventino = them/they become
best website ever for verb conjugation: http://italian-verbs.com/italian-verbs/conjugation.php?parola=diventare
The Subjunctive mood expresses doubt, uncertainty, hope, fear, possibility, opinions, etc. and is used much more frequently in Italian. It is mainly used in dependent clauses (sentences introduced by a conjunction that do not have a complete meaning) that are introduced by che.