You need enough gas out of the pump to keep the carb bowl full. Check for a clogged fuel filter or cracked/leaking "pulse" hose. The cut off solenoid is probably on the bottom of your carb. Hint- it has an electric wire going to it. It doesn't have anything to do with gas getting TO the carb, Just gas getting THROUGH the carb.

The correct method is to replace the flywheel should the magnets be loose. I've seen the magnets chew everything to bits to causing no damage at all. Some will epoxy magnets back on, but I never have. The risk for big damage is there. I had a single a couple of weeks ago that had 1 VAC output that I had briefly flashed the 12v over to the AC and it charged and stayed that way so far. Never expected it to really. Figured I needed a stator. May yet. Other than that, it comes apart.

To replace a rod, you have to remove the head and push the rod/piston assembly out of the block. Before you do that though, you have to remove any wear "ridge" that may have formed in the cylinder at the height where the upper piston ring travels. Failure to do so can break rings (possibly piston), since the rings will "catch" on the ridge. IF one gets THAT involved, it's almost a shame not to install new rings. IF you do it on one cylinder, it pretty much makes sense to do it on both.... What I would do-? IF the rod bolts didn't thread back on smoothly, I'd probably replace them. THOROUGHLY examine the rod & crank bearing surfaces for ANY gouging or metal DEPOSIT (on the crank). IF every thing looks OK, I'd button it back up and use it. Like I mentioned earlier, I'd start off slow and work your way "up" on the throttle for a minute or so and back for the first 15-30 minutes. Go up to speed a bit more each time and then idle. REPEAT until you are up to full throttle. LISTEN for the start of any noise. If you hear anything "abnormal at any time, shut it down. If not, go mow. If you make it through the first hour of mowing, you're probably good.

Hard bumps, huh? You might be looking for something mechanically loose like engine mounting bolts or a bad ground or marginal electrical connection. Don't overlook that a wire can fray or break just ahead of a connector and be REALLY hard to spot. Get the battery load tested to make sure it is good. Check BOTH battery cables at both ends and the starter bolts to make sure they are clean and tight. Check the safety interlock switches for proper operation and adjustment. Check the connections at the back of the ignition switch and make sure the fuses have clean and tight connections. Sit down and carefully inspect the tractor from front to back and up to down for anything loose.