Woods 1250 mow n machine starts and runs fine-once. When shut off it won't restart for about half an hour. Doesn't matter if it was running 2 hours or 2 minutes, it won't restart.

SOURCE: Sears 19 hp twin 42 inch tractor, won't start if hot

Hi
Two things come to mind. First it could be not getting enough fuel when hot due to carb adjustment being too lean. That could be that the float level in the carb is set too low or the low speed jet is set too lean. When cold the choke circuit in the carb supplies the extra fuel required.
Second in some enjines that have low compression they start cold but when hot the compression drops below 60 psi and makes starting very difficult until engine cools down.
I suspect a fuel problem.

SOURCE: 96 cub cadet 2140 with cummins onan 14hp

I have cummins cub cadet Onan Elite 140 engine shuts off after about 20 min and won't restart for half hour.

SOURCE: mower will not go forward .... it runs .... and the deck still engages but will not move forward or backward

i would inspect the belt the mower and the trans operate from different belts

SOURCE: Craftsman 26 hp Kohler engine 54

to be honest the enigne ahas a control that the left side must fire and run before the right starts to fire it sounds to me like you have a fuel issue possibly the carb. is gummed up and dirty.

SOURCE: Mower will start up cold, i will mow for a half

Try cleaning out your gas cap - if debris gets in the holes in the cap it will eventually cause a suction in the tank preventing fuel from getting to carb and engine. Any doubts, try running with the gas cap off and see if that does the trick.