Welcome. The 110 originally came with a 22x11x8 all the way around. Be patient on ebay. Should be able to find one for a lot less than what you are seeing. You could get by with a tube from a 70-82 90-110. They are made a little different through the years but all should work. As far as the china carb.....they can be hit or miss. I would just clean the original carb. If you need parts you can purchase a rebuild kit for little money.
Good Luck!
* 1978 ATC 90/180 Pauter PJ1 / Springer "Team BAPP" Bike *
* 1980 ATC 110/180 "Danny's Machine Works" 3D Sprint Dune Bike *
* Nicholson 500 Race Bike *
* HPATC Yamaha RD350 "Big Moe" Trike *