Let's begin with the tappet clearance:

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The yellow ovals show the junction between the bottom of the valve stem, and the top of the tappet. (I've turned your picture around so that "up" and "down" mean what they would mean on a horizontal crankshaft engine.) Be sure you have the engine rotated to a little past top dead center on the compression stroke - Briggs used a feature called "Ezyspin" which holds the inlet valve slightly open during the compression stroke, to make the engine easier to pull-start, and it is important to rotate the engine past TDC to ensure it is not still operating when you measure the clearance.

I agree with your metric conversion results, so it appears that your inlet tappet may be at least slightly overly tight, unless you find you can increase it by rotating the engine forward a bit more from top dead center. I would like to see a more precise measurement than just finding that a 0.1 mm gauge (0.0039") will not fit in the gap. The exhaust may or may not be tight - you would need a feeler gauge of 0.009" to find out for sure. To correct the inlet valve clearance it is necessary to remove the cylinder head, remove the valve, and grind the end of the valve stem slightly shorter, keeping the grinding exactly at right angles to the axis of the stem. This is a fairly awkward process, because if you grind away too much you have to replace the valve, it can't be made longer again. So, if you are interested in learning more about small engine maintenance, you should consider rechecking the inlet with the engine rotated a bit further beyond TDC, and if this confirms that the clearance is inadequate, dismantle both valves and lap or grind the stems. If you decide to do this, we can talk in more detail about how to do it.

I cannot guess at this point whether your engine would run better with the clearances corrected. It appears that they are below minimum specification, but in general this clearance is not critical unless it is close to zero for the inlet, and less than say 0.003" for the exhaust. Nevertheless on a side valve engine like yours the clearance tends to decrease with time as the valve works its way deeper into the valve seat (where the valve head seals against the engine's cylinder, inside the combustion chamber) so insufficient clearance in a new engine is quite undesirable.