There is no luggage storage counter in Guilin airport. You can try to check you luggage at the airport hotel.

Yes there is but it's not obvious. I had to ask at the Information Counter with my request written in Chinese. When I first asked in English they didn't fully understand. It cost 10yuan a day and the desk is open from 7am until 10:30pm so they said. They will give you a ticket a stub, put the bag thru the scanner at the normal baggage check-in, and then bring you to a locked room to store it. Ittook maybe 20 minutes I'm total.