We need to see it in a sentence, to know how to answer your question. Susan is right about the "party" meaning, but the verb "to rave" has several meanings that are not related to "raves" as parties.

An important point about "would." It is used in the case involving a condition. "IF" x, then I WOULD "Y." I want to go fishing, but my wife WON'T (WILL NOT) let me. IF my wife would let me, I WOULD go fishing. IF I asked her whether I could go fishing, she WOULD say "no."

Is it a deal? or Have we got a deal? "A" deal. Then, later, if you are discussing the matter (asunto), you would refer to the deal as "THE" deal: What is the deal you made with Jaime? The same as in Spanish: "¿Tenemos UN trato?" and (depues) "EL trato que hicimos dispone que...."

Due to the death of a close family member, I am writing to request permission to be absent from work until noon tomorrow morning.

I think you mean "Is this a phrase common in English....." The word "auditors," in the context of business, means "examine and verify the financial records of a business," so that "business audit" is a redundant phrase. That is, the word "business" is not necessary and adds no information or meaning to the word "audit" itself. If anything, one would say "audit the books" of Business X. "Books" meaning financial records. Of course, those records are on computers now, but the phrase originated when financial records were kept in physical, paper, books.

"Have no intention" is not a phrase that you would use in a friendly way. It's not hostile or unfriendly by itself, but it is a pretty formal way of speaking. It is almost a defiant word, denying that you intend to do something (bad or hurtful) that someone has said that you are going to do. It says "I deny that I am going to do what you have just said I will do," or (and this is different) "I am not going to do what you have just ordered or demanded that I do." "I don't (or, much more likely "didn't") mean to hurt your feelings" is usually an apologetic statement, by which you are saying that you feel bad that you did something that caused the other person to feel sad or demeaned somehow. It is a very personal statement, from one person to another. The "no intention" statement does not suggest a close personal relationship between the two people.. I can't really think of a situation when someone would say "I'm not going to hurt your feelings." Hurt feelings are a result, a consequence, of something that someone does. "To hurt someone's feelings" is not -- itself-- something that one does. In a situation like this, they really would say "I'm not going to [do whatever it is that would cause the hurt feelings, such as "insult your family" or "tell you that you are dumb."]"

John le Carré and Ian Fleming wrote novels about British intelligence operations. Their novels were very popular, and so were the main characters in them, who were British intelligence officers. So: If a British intelligence officer goes anywhere in the world, all he has to do is to introduce himself (tell who he is and what work he does-- an officer of British intelligence) and his work would be understood and he would be expected to be like one of the characters from the novels. So he would be recognized -- his job would be understood-- but he might not really be welcome, since his work is to be a spy. A "calling card" is a little card -- a business card, we usually call them -- with a person's name, company, and phone number.

He withdrew his arm" or "He drew his arm back."