Kawasaki KE100 problems..?

Not sure what you mean by bogging down;

Worst case first, it is the piston about to seize. Check you have two stroke oil and that the pump is delivering it.

Engine cutting out when hot is also a classic coil and condenser symptom so check (replace) those.

Left field check the choke is not on, or it will not run properly when warm.

Check you have the right spark plug fitted. Two-strokes are sensitive to that.

Service the plug, air cleaner and fuel system, from tank vent, fuel tap filer screen, check hoses for kinks.

Don t go tuning and making the bike unreliable. It is a 100cc. You want more power, buy a new bike or learn to ride the one you got proper (as my old nanna used to say)

New plug.

Check the cap to be sure it's venting.

Check the fuel flow.

Check all rubber on the intake boot/carb socket/ect.

Clean the carb- AGAIN. Last fall was a long time ago.

Worry about getting it running RIGHT before you worry about "making more power".

The fuel starvation is likely a clogged fuel-tank vent in the cap, the clog causes a vacuum so fuel flows very slowly, once you've stopped fuel seaps back in and you start all over again,. Clean the cap.

Probably the same sorta problem for lack of power, CLEAN things up. Air filter included.

Symptom of a defective ignition coil.

Check for spark at the spark plug when the engine won't run.