Specifically, check inside the elbow at the bottom of the fuel tank. MANY of those here have ended up with chunks of sealant in there left over from tank manufacture.
The backfiring and dieseling (running after shutdown) is normal. The exhaust manifold is insanely hot because the exhaust header and muffler are poorly designed. If you do a little searching you will find that quite a few of us have got rid of the stock header and muffler and replaced it with the Robin header and muffler, which seems to help.
These little tractors have problems with vapor lock, although it seems that it is probably cool enough out (YMMV) that this shouldn't be as much of an issue. The fuel pump is mounted on the same side of the tractor as the muffler, which seems to contribute to this...easy enough to relocate the pump.... nothing magical about that location. The pump is driven by pulsating pressure through a 1/4" line plumbed off the crankcase. You can put the pump anywhere you want.
I wish I'd have paid more attention to my new gas tank instead of assuming it was clean.
I may look into relocating gas pump. I was hoping the heat wouldn't be as much of an issue on these newer designs with muffler outside of hood.