When you submit your passport for Visa now in China, you receive a paper which will serve as your visa for things like hotel check-ins etc. It is a better more functional paper which shows more information about your visa application as well as your face, so that part of your problem is taken care of by default 😀
They can issue a 30 day travel visa (I heard first one can be longer..but that it’s almost always just a 30 day extension) but you have to prove you have cash available for the remainder of your trip, so ensure you have bank balance with maybe 20k RMB? or more available to show them if they ask. Right now, Visa applications and extensions take up to 3 (yes up to THREE) weeks. My recent visa renewal took 3 f’n weeks. (15 business days). A simple L visa extension may take less time, but it depends on a lot of factors, you’d find out upon arrival.. I suggest going to the PSB your first week in Chengdu just to be sure.
Lastly, why would your travel agency get you a 20 day visa? I didn’t even know 20 day visas existed – thought minimum L visa was a month, and the only shorter one was a couple-day transit visa you can pick up in Shenzhen.