Recharge the battery .
Get a can of carb cleaner and go mow
when it won't restart squirt a SMALL amount of carb cleaner down the carb and see if it fires
You should not need to turn the mower off to open a gate
When the parking brake is set you should be able to get off & leave the engine running, provided that the blades are off .
Not a fix but a work around till we figure out what your problem is .