This is a clarification strategy used to confirm the understood message. After saying this, Dan can be 100% sure that the message he understood is the same as the message Kay intended. If there was any misunderstanding, it could easily be cleared up at this point. Now that Dan is sure he understands the details, he can accept the invitation.
"I hope you can make it?"
Kay is expressing her hope that Dan can come; while at the same time, she is asking Dan to respond whether he can or not. By asking in this way, Dan can give a number of replies--Yes, No, Maybe, We'll see, Me too, etc. Kay doesn't make Dan feel that he must give her his answer right now--perhaps pressuring him or making him uncomfortable. She is being polite.
"I'll be there with bells on."
He is telling Kay that he will be there, but also he is letting her know he is excited about it and will be there on time. ("with bells on" is an American idiom which means to be excited about the event and will be there exactly on time.)
"Can I bring anything?"
In most informal situations it is considered a common courtesy to ask the hostess this. Often the reply will be "no, but thank you for asking" or "if you like, but it's not necessary". Regardless of the hostess's reply, it is a friendly gesture on your part to take some wine, flowers, candy or even just potato chips--depending on the situation.
"I'm looking forward to it."
This is a polite conversation close. It says he won't forget, while signalling there is no more to say now.
"Thanks for inviting me. I brought some wine."
These two go together--each complementing the other. He is not only expressing his pleasure with words, but also reinforces the words with a gift. By saying this combination, neither Dan or Kay are left stumbling with who should say what about the wine which is obviously in Dan's arms.
"Let me introduce you to..."
Introductions are politely done in a particular form and with a specific pattern of words. 99% of the time an introduction will go as follows:
"Dan, let me introduce you to Claire."
"Claire, meet Dan."
The names are repeated as such to help the two parties to remember them. This form also implies an equality of the two parties. Often an explanation or connection is given for how the person doing the introducing has come to know the two. In Bill's case, he tells Dan that Claire is his niece and tells Claire that Dan works with him in his office.
"What part of the East, Claire?"
By asking a general question of Claire that follows up on a previous part of the conversation, Dan is showing interest in getting to know Claire better. And by using her name at the end, Dan is not only reinforcing his memory of her name, but also letting Claire know he was interested enough in her to remember her name.
"It must be quite a change --coming back here?"
Dan is again asking Claire a question which shows his interest in her, and also the question is stated in such a way as to now give Claire the opportunity to tell Dan more about herself. If she wishes to let him know more about her she can now do so easily. If she does not, she is not in an awkward position of having to either answer a very specific question or stumble to find a way to avoid it.
"I'm glad to be back and see all of my friends."
Claire chose to answer Dan's question in a very non-revealing way. With these words, Claire is saying "One good thing about being back is seeing my friends," and no more. She isn't forced to reply about any personal reasons for why she came back; however, if she would have liked to, the question would have allowed her to easily do so.
"Do you still play golf?"
Hobbies such as sports are often a way to begin a conversation with someone. When someone plays a particular sport, they are usually glad to talk about it and it is an easy way to make a common interest known. Bill not only asks Dan about a sport he plays, but Bill knows that it is a common interest of the three coversation participants and that they all could feel comfortable talking about it.
"Not as much as I would like."
Dan could have simply answered "Yes" or "No", but by replying this way he also conveys that he would like to play more. This gives Bill the opportunity to come back with a suggestion that they go and play sometime--a suggestion that Dan was probably hoping for when he chose which words to say.
"I see you've met Elizabeth."
This is a very easy way to enter into an already-in-progress conversation. It requires a response and that requires a break in the conversation-in-progress.
"Elizabeth? I thought your name was Claire."
Dan has just been given a very confusing message. He needs to sort it out. The clarification strategy used here is very direct and to the point--this woman in front of him has been called by two different names and he wants to know why.
"Could you pass me that newspaper?"
By beginning with "could" this is asking,"Is it possible?". It is a polite way to make a request. But notice even though it is very polite there is no "please" used. "Please" may have been included, but it is common among close friends to drop it in a casual situation. With it, the request would seem more formal and since "could" was used it was not as formal as a request such as, "Please pass me the newspaper."
"Sure, here you go."
An informal answer to an informal request is appropriate. This answer implies that he doesn't mind at all--helping the requester to not feel uncomfortable asking for the assistance.
"How often do you play, Dan?"
Claire is now showing interest in knowing more about Dan. The question is not personal, but the reply could provide her with some clues into Dan's lifestyle. The theme of golf is used because it has already been seen to be an agreeable topic. You should be careful not to "wear out" a topic, however.
"How about you?"
When someone asks you a "How do you..." type question, 99% of the time the appropriate response is to first answer, then ask "How about you?" or "And you?". By doing this you will show that you are interested in others' choices or opinions.
"Enough about golf! How's your dancing?"
Kay is showing her disinterest in talking about golf and that she wants a change of topic. It is also clear that she does not simply want to know about your dancing. She wants you to actually dance with her. Since party's usually have music and an environment which would be suitable for dancing, this approach is very effective for changing the tone of the conversation as well as for getting a dance partner.