I don't get an image from either of your videos. If the crankshaft endfloat is over 1 mm, it means the engine is defective. The crankpin is only 1.1 mm wider than the connecting rod, so the crankshaft is moving far enough to cause the connecting rod to be pulled too far sideways, which could cause a variety of bad things to happen to the rod and piston. It can't happen due to the crankshaft being bent, though it could happen if the crankshaft has been compressed axially in a press. I'd say it is either wear or defective parts, unless the engine has been damaged in an unusual way.
I can't interpret your comments to understand what you mean regarding vibration. If the engine blows blue exhaust smoke, the engine has a problem and is leaking oil into the combustion chamber. There are several possible causes of this. Black exhaust smoke would probably be a result of running the engine with the choke operating, or when the carburetor had been flooding.
