THAT DON'T IMPRESS ME= That doesn't make me think you're great and important. Yes, THAT is third person singular, so the verb should take an -S (that doesn't impress me), but in colloquial English people sometimes forget about the -S for the 3rd person singular, especially with the auxiliary verb DO (e.g. "she don't like me").

GUYS (coll. AmE)= men.

SMART (AmE) = intelligent (BrE). In BrE "smart" means "elegant".

YOU’VE GOT BEING RIGHT DOWN TO AN ART= You always want to be right. You try so hard to be right all the time that you have turned it into something sophisticated, like an art. YOU’VE GOT = "you consider". BEING is used here as a noun, like in: "Being right is an art", where "being right" is the subject of the sentence.

YOU DRIVE ME UP THE WALL= You make me feel very angry, nervous, irritated.

YOU’RE A REGULAR ORIGINAL= Most people think they’re very original, and you’re just one of them. REGULAR means "common, usual, ordinary, normal". What she means by that is that he thinks he's original but he's not.

A KNOW-IT-ALL= A person who thinks they know everything (pejorative word).

A ROCKET SCIENTIST= A scientist who designs rockets. A rocket is a aircraft designed to travel into space. See a picture here: a rocket.

YOU GOT THE BRAINS= You’ve got the brains = you are very intelligent.

HAVE YOU GOT THE TOUCH?= Have you got what I need?, are you the right person?
To have the touch is to have the right ability or personality, to be the right person for that situation. "The touch" is the same as "a je-ne-se-quoi", but the French expression sounds a bit pedantic (though many people use it, esp. in the UK).
She’s looking for a guy who has "the touch", which in this particular context means that he is a nice loving person able to make her happy.

DON’T GET ME WRONG= Don’t misinterpret what I say. You use this expression when you say something that may sound offensive but you don’t want them to be offended. So most of the times, if you use this expression it’s because you are being offensive.

COMB= a tool to make your hair look tidy (see picture of a comb). Pronounced /kəʊm/, remember that words ending in –MB have a silent B (e.g. lamb, bomb, plumb, etc). The verb is also "to comb your hair".

UP HIS SLEEVE= Literally it means "under your sleeve". The SLEEVE is the part of a sweater or jacket that covers your arms. When you put something inside your sleeve, you pull it up from your wrist upwards, so we say "UP the sleeve" and not "under", that should be the correct form. We also use the expression "to have something up your sleeve" meaning that you carry something at hand, ready to use any moment, even if it’s not actually up your sleeve but in your pocket or wherever.

JUST IN CASE= Because you may need it, though that’s not probable.

EXTRA HOLD GEL= A hair gel (to keep your hairstyle in place) which is very powerful and makes your hair almost solid.

OUGHTTA (coll.)= Ought to = Should

LOCK= To lock your hair with gel is to fix it in place using gel so that it won’t move and your hairstyle won’t change.

‘CAUSE= Because. Also spelled: ‘coz, ‘cuz, ‘cos.

OUTTA (coll.)= Out of.

OUT OF PLACE= Untidy, not neat, not in order.

HEAVEN FORBID= As an expression it means "I really hope that will never happen":
- If you keep driving so fast you’ll have an accident some day. Heaven forbid!
"Heaven" is a euphemism that means "God".
But when this phrase is part of a sentence, like here, it means, "it would be horrible if that should happen":
- Heaven forbid it should fall outta place = It would be a disaster if your hairstyle is ruined.

YOU GOT THE LOOKS= You are so attractive, so handsome/beautiful.

TO SHINE HIS MACHINE= To polish his car until it shines.

TO KISS SOMEBODY GOODNIGHT= To say good-night with a kiss.

C’MON= Come on!

YOU MUST BE JOKING, RIGHT?= This is a joke, you’re not serious. Notice how we use RIGHT at the end of a sentence instead of a question tag.
- You’re Brazilian, aren’t you? = You’re Brazilian, right?
- He can speak German, can’t he? = He can speak German, right?
- They don’t know me, do they? = They don’t know me, right?
Question tags are more common in the UK and right-tags are more common in the USA (and they’re very simple, so please, if you speak a romance language, like Spanish, Portuguese, Italian, French, etc, stop saying: "You’re John, no?" and say "You’re John, right?", it’s just as simple and it’s correct!)

YOU’VE GOT THE MOVES= In this context, talking about the guy with a car, it means "you can go with your car wherever you want". In a more general context, "you've got the moves" may mean "you know how to move, you move in a cool way, I like the way you move".

COOL= Great, fantastic, fashion.

YOU’RE ELVIS OR SOMETHING?= We use the phrase OR SOMETHING? at the end of a sentence meaning "or something similar to that".

WHATEVER!= As an expression it means: "Ok, I don’t want to argue with you about that because I don’t care about it. I think discussing about this would be stupid, so I’m not going to say anything else":
- You should do something with your hair, it looks horrible
- No, it’s not. I looks nice to me.
- Nice? Oh gosh, you look like a hippie from the 60’s.
- Yeah, right. Whatever! (end of conversation)