Should I fly a plane just after a new cylinder was installed?

The A&P would have taken it for a test flight and put it through all necessary testing in order to certify it as airworthy before it was returned to you. If it wasn't safe to fly, you wouldn't have the plane back.

Cyclinders are fine. I would avoid cones till you are in the air as a great deal of concentration is needed to actually take off and wind the wheels in.

I doubt that your instructor has any more experience with "off-airport" landings than YOU do, Skippy. Nowhere in the training to acquire a commercial pilot's license and CFI rating is there a requirement to land an airplane in a corn field or crash into a forest.

it's just a cylinder, piston and ring overhaul? The break in procedure is very fast. Engine bearings, on the other hand are different.

Cylinder ring seat procedure is........

Hard acceleration and deceleration ten times. This will seat the rings. The load a vacuum pressures push the rings out to seat against the cylinder wall.

check your brakes first

1] It should be flown by someone who knows how to properly break it in.

2] Good luck finding an instructor who has done an actual off-airport landing. For the vast majority it's only theoretical.