The first sentence sets the tone of novel because the register is highly formal due to the title sir" and "may I"

The expression "don't be frightened by my bear" is unclear because if someone you have never seen before   wants to have a tea with you, he should not be scared. So why does the narrator tell him not to be frightened?

A key word in this chapter is "mission". Indeed, the narrator asked the stranger if he is on a  mission. The reader understands the importance of that word in the last chapter, especially in the last scene.  

The narrator suggest that the stranger is an american because of his bearing. This fact lets the narrator to tell him that "he is a lover of his country" to increase the Stranger confidence and to introduce his past story which is sets in USA.

Moreover, the stranger decides to seat  "with his back close to the wall" and he does not want to remove his jacket, suggesting the reader that he is probably an agent. This concept is underlined again when the waiter appears: The narrator tells the stranger that "there is no need to reach under your jacket, I assume to grasp your wallet, as we will pay him later, when we are done". This sentence is relevant to understand the end of the novel. The intelligent reader has to ask himself what if  the stranger was not looking for his wallet but he was reaching something else in his jacket?.

While the narrator is talking about his past experiences in America, at some point he speaks about a value firm he works for, the Underwood & Samson, after he graduated at Princeton. He tells the Stranger that he had an interview before he started working for the firm, and this is the first time the narrator reveals his name , Changez. This situation is strange, because when you are about to speak with someone you don't know, you usually introduce yourself before you start talking with him. But in the novel, the narrator mentions his name after a while, to increase the reader curiosity. It makes the reader to think that probably the Stranger will also reveal his name, but this will never happen.

Then the Stranger seems suspicious again. Indeed, when the waiter brings them the tea, he wants to switch his cup with Changez one, in order to be sure that what he is going to drink is not poisoned. This fact is also strange, because the Stranger wants to have a tea with Changez but he is still scared.