I want to test for allergies in a hospital in Kunming. I have found a hospital where I could get tested, but they only do blood tests ("because of hygiene"). These are not very reliable.
Does anyone know of a hospital where they can do a standard skin prick allergy test?
I think you will definitely need a temporary residence permit to get an extension for your visa. If you are staying with a friend then you should have gone to the police station within 24 hours to register your stay, after which they would have given you the residence permit.
If you don't have this permit, it might be a good idea to pay for one night in a cheap hotel, and show your hotel receipt to the visa officer (and not mention your friend anymore).
If you do have a temporary residence permit, they may need to see your friend's rental contract as well (or ownership papers if he bought it). They may also need his passport. I also don't think a letter from the landlord is necessary. Sometimes the visa officer will ask for something out of the ordinary, but when you go back (and get another person) they don't need it.
You will normally also need to write a letter at the visa office, stating the reason(s) why you want an extension.