I asked a question a few days ago, but now I am confused again. I am an American citizen. I want to go to China on October 7. My Korean ARC expires on October 27. So, from what I've been hearing, I need to apply for my visa 6 months before my ARC expires, so I need to apply in the next few weeks. BUT, what kind of visa can I even get applying this far in advance?

Also, what does it mean that I need a letter of invitation from the friends I am staying with? Does it need to be official or can it be an email? And if it needs to be official can it be scanned and emailed to me? They said they've never had to provide any of their visitors with this letter of invitation. PLEASE HELP!