Dear Wang Feng,
I am glad to know that you are adjusting your life in America. I believe that the difficulties you've found are very good opportunities for you to learn from.
First, let's talk about handshake. People form opinions about a person from his handshake, specially when they first meet. In America, people usually regard giving really limp handshake as having no confidence and often think that they are not reliable. Besides, there is only one proper handshake and that is a firm handshake, simply put-- Extend your hand, make sure the web of your hand makes contact with the web of the other's hand; close your thumb over the back of his hand; give a slight squeeze with your fingers; Two quick pumps and let go. No wonder your American friend had an odd face when you didn't give pressure at all when clasping hands.
The other problem you mentioned in the letter refers to punctuality. Punctuality is important in America. It simply means being on time. If your appointment with friends is confirmed at one o'clock, you are expected to show up at that time. Being late is a sign of disrespect. Suppose you had to handle with an abrupt change and couldn't make it, inform your friends that you are delayed. This can make them feel being respeccted. Anyway, you'd better not let this kind of thing happen and be punctual in the future.
I hope you can get along well with your new friends soon.