The oil in the cylinder could be how it was stored. Reason I say this is because I was shipped an engine that was supposed to have no oil in it and during shipping, with "this side up" stickers on the box, it apparently was in the cylinder down position and had oil in it. I installed it and when I tried to crank w/ the starter it locked up. I removed the plug and hit the starter and it shot oil 8 ft across the shop floor. Once I got the gas rinsed out of the cylinder and got it started it blew a lot of blue smoke for awhile and has been fine ever since.
The hard starting after running could be the same problem I solved with the new engine I put on my chipper. It would start fine when cold but restarting after running was b!tch. I finally deduced that the spark plug worked fine while running but when it was stopped the plug would soak up heat from the head and short out. A new plug fixed that problem.