It is a way to put emphasis on the YOU, = "How are YOU?". ...or just like Dalaryn said above, a way to be polite.
It is for emphasis - it's common in French too, which I see you're studying :) Like you could say, toi tu vas bien? And it's just emphasising the you.
"Wewe hujambo?" is the short form of "Wewe hauna jambo?"
In this context 'jambo' means 'problem'
and Hauna jambo? is as follows:
You = Wewe u; have = na; problem (jambo)
Wewe u-na-jambo = You have problem
The negative is then made by fixing 'ha' before subject marker prefix 'u' to get:
Wewe hauna jambo can be shortened to Wewe hujambo?
Wewe hujambo = Don't you have problem?
Don't you have a problem, so how are you?
I see some of these don't have the pronoun in front of them... are the pronouns needed or can you omit them?
It's polite to use them the first time you address someone (including yourself) in a conversation. They technically are not needed and aren't used after the first reference to them.
What's the difference between hujambo and hamjambo? They both mean the same thing?
hujambo is 2nd person singular (talking to one person), hamjambo is 2nd person plural (talking to multiple people)
"Wewe" means "You" but when I submitted the answer of "You how are you" It was incorrect.
In English people sometimes say "what's up?" or even just the " 'sup?" as they walk by another person, but aren't really asking a question. It is technically a question, but really just meant to be an alternative to "hi."
It's the same here: "Wewe hujambo?" is shortened to "hujambo?" which is further shortened to "jambo" (mostly just by tourists). It is technically a question, but also used to say "hi."
Hujambo is how are you. Wewe comes from English constructions. The combination is used when talking in a group and you single somebody out.