Can somone tell how a lawn mower would act if the coil was gone or weak?
and how to test it?

If the coil is bad it would not produce any ignition spark, an ignition coil of the type found on most small engines, either work or they don't. There can be instances where a coil may loose spark as it gets hot, but they do not "wear out" as there are no moving parts in a coil.

Over a period of time the insulation surrounding the coil windings can crack and allow moisture to enter. The expanding and contracting from high to low temperatures can cause a break in the coil windings, and overheating can cause the insulation on the windings to melt and cause a coil to fail.