Jerry, please read Bruce's comments carefully - he has repaired more mowers even than Joe Carroll, and he knows whereof he speaks. Also, remember that while your ignition coil does not seem to be the problem right now (if choking it consistently improves its running), it is a known weak link in your engine's reliability.

Because you don't have a fuel filter in the tank, you are at risk of having a blockage in the carburetor fuel intake upstream of the needle-and-seat: the funnel strainer is way too coarse to do the job the fuel filter does.

The inlet pipe is the tube from the carburetor to the engine's intake port: if it were on a multi-cylinder engine it would be called the inlet manifold, but on a single cylinder engine it is the intake pipe. It is under vacuum when the engine is running, and any hoses that run off from it can be a source of vacuum leaks if they are missing, split, or disconnected at the other end.

Having said all that, the single most likely cause of your problem is dirt in the main jet, which is the external, screwed-in device that holds the vertical plastic disk that is the side of your float bowl. A plastic carburetor guy (not me of course) would be suggesting, given that you don't have a fuel filter, that you begin by removing that and blowing it clean. See "jet assembly standard" in this diagram:
[Linked Image]