DO YOU MIND +ing= We use this phrase to ask for a favour.

KEEP IT DOWN= Don't make so much noise; speak softly.

SALSA= A Latin rhythm from South America.

CAN'T GET THE MUSIC OUT OF MY HEAD= Can't stop hearing that song inside my head.

CAN YOU NOT?= The usual thing would be "can't you?", but using it without contraction sounds much more formal, polite or sarcastic.
As you can notice, in this conversation the blond lady uses these kinds of question tags very often to express interest in the conversation. In this case she has no real interest, she just pretends to be interested because she wants to be polite. But normally these tags are used to show real interest. And it's also a good way to keep the conversation going when you don't know what to say.

NEVER THOUGHT OF MYSELF AS A DANCER= I never thought I could dance well.

TURNS OUT= If something turns out in a certain way, it happens that way, which is surprising and/or unexpected.
- I thought Susan was really stupid, but we spent the day together and she turned out to be quite nice.

INSTRUCTOR= In this case it means "dance teacher".

TONY?= Notice that Catherine is pronouncing the name Tony with a Spanish accent, which in English sounds like "Donnee". That's why the other lady is confused about what she means with that word.

RIO= The Brazilian city of Rio de Janeiro. They speak Portuguese in Rio, and salsa is a Brazilian dance, though it is also quite popular in Caribbean countries. The song "La Bamba" is Mexican and so the lyrics are in Spanish. Then she will talk about Barcelona, in Spain. For an English person, Brazil, Mexico, Cuba or even Spain are just the same culture and the same language, so all this mixture is perfectly fine for them.

PRAISING= When you praise someone you tell them nice things about them (e.g. "you're nice and lovely and beautiful, I like you, you're the best.")

GAZELLE= An African animal from the savannah who moves fast and gracefully (see picture).

WORKSHOPS= An educational seminar or series of meetings emphasizing interaction and exchange of information among a usually small number of participants. In this case she refers to dance workshops.

COMPLIMENTARY= If you are complimentary, you say compliments. A compliment is a nice thing you say about one person. Complimentary is the adjective, compliment is the noun and to praise is the verb (or to make a compliment).

ACTUALLY= In fact.

GUESS= If you guess something, you predict or estimate something although you have no information or not enough information for it.

GUESS HOW OLD HE THOUGHT...= There is no inversion in this sentence because it's not a direct question (the rule is: no question mark, no inversion).
- How old is she? (inversion)
- Tell me how old she is. (no inversion)

HAVE A GUESS= Guess.

THAT'S THE POINT OF...= That is the interesting thing or the useful thing of...
We say "guessing" in the –ing form because after prepositions and conjunctions we have to use the verb in the –ing form.

DON'T MAKE ME DO THIS= Don't force me to do it.

I DON'T WANT TO= I don't want to guess.
The particle TO can be used as a "proverb". In the same way as a pronoun is substituting the noun, a proverb can substitute a verb (and its complements):
- The book is there. Take it  (IT = the book).
- He wants to drink beer but I don't want to  (TO = to drink beer)

BLIND= A blind person can't see.

VANESSA FELTZ= A well known radio and TV host in the UK. She doesn't look attractive at all and looks older than her age. That's why Catherine feels insulted in the comparison. (see picture)

NEITHER DOES TONY= You don't think so and Tony doesn't think so.
- You are French and so is Kevin = You're French and Kevin is French too.
- You are not Italian and neither is Kevin = You aren't Italian and Kevin isn't Italian.

NOT THAT OLD= Not so old.
In some negative sentences we can use THAT instead of SO in colloquial English.
- I'm not that stupid = I'm not so stupid.

RIGHT= Catherine uses the word "right" a few times in this conversation with the meaning of "alright, ok". This is very common.

I DON'T THINK SO= (coll.) No.
This is a colloquial phrase to say "No". It is Bart Simpson who made it very popular because it was one of his favourite phrases.
- Excuse me, are you Peter Mason?
- I don't think so.

FLATTERING= If somebody tells you something flattering, they tell you something very good about you, sometimes insincerely, to make you feel happy (sometimes just because they want to get a favour from you).

I USED TO...= We use this phrase to talk about a past habit that doesn't exist in the present anymore.
- I used to play football when I was young (but now I don't)

TAP= Tap dance = A dance in which the rhythm is sounded out by the clicking taps on the heels and toes of a dancer's shoes.

DO YOU EVER STOP TALKING?= You never stop talking. You're always talking. Stop talking!