"Why do some FFLs refuse to take a shipment from an non FFL? Is it illegal for a non FFL to ship a gun to an FFL?"
Because they are ignorant to read the rules and make them up.The other one some FFL's make up is you must send a drivers license with the gun.If you stole the gun and sold it do they really think they would get "your" drivers license?
"If I wish to sell a gun to a friend and we both go to an FFL to do the transfer the rules have been complied with and there is no problem. Right?"
Not sure about Kalif but for most states in the US there is no need to have any FFL involved for sale between two residents (as long as neither are felons or prohibited from owning a gun).