Peter, the valve clearances need to be as Honda prescribed. If they are less, the valves will leak some or all of the time, and leaking valves erode and leak more. The reason for annual adjustment is the number of wearing surfaces in a pushrod valve train, and the relative flimsiness of the parts concerned, compared with a simple side-valve valve train. Excessive valve clearance is a bad idea, though not as bad as insufficient clearance. Aside from noise and an increased wear rate due to the recurrent impacts as the valves open, the decompressor can't work if the exhaust valve clearance is substantially more than it should be. The main disadvantage of pushrod engines compared with side valve ones, is their need for more regular, and more expert, maintenance. They reward us for that extra maintenance of course, by running much better and using much less fuel.
If they are not leaking air through the insulator gaskets, and the carburetors are clean, pushrod Hondas should be able to idle fairly nicely down to about 1,500 rpm. To make them idle slower than that you would need to have variable ignition timing, which Honda puts on the postie bikes but not on the mower engines. One of the reasons for that omission is cost, but it is also important that Honda does not want the mower engines to be run slowly, because of heat soak-back. When an engine has been running hard under load for a longish time, it gets up to maximum safe operating temperature, and when you take the load off it, it does not cool down instantly. If you reduce the fan speed immediately after taking the load off the engine, the temperatures will actually rise quite substantially, due to the thermal inertia of the parts involved. Consequently it is important that a mower's operator cannot suddenly reduce its speed to an extent that almost eliminates the flow of cooling air from the fan. Of course this problem is almost non-existent with water-cooled engines, but mower engines are air cooled for reasons of weight and cost. So, Honda tells you to set the idle speed of GXV120 and GXV140 engines at about 2,000 rpm, although they will idle well at much lower speeds.
Your engine does not have the thick carburetor insulator of the GXV160. I cannot see the intake port, so I can't tell whether it is square (GXV160), D-shaped (GXV140) or round (GXV120). However we can't be sure a chonda manufacturer won't have deviated from Honda's base engine design, though I haven't heard of that happening up to now.
Chondas seem to always have their own idiosyncratic air cleaner designs, probably for reasons of visual differentiation of their engines. The usual rule for paper-element air cleaners is that you do not oil the paper element, but you do oil the foam pre-filter. However there are such things as oiled paper elements, and dry pre-filters, for reasons best known to their designers. Essentially, you can't reliably and repeatedly clean an oiled paper filter, though I've done it successfully to a dry paper element that became completely oil-fouled on a worn, smoky engine. It sometimes works on good-quality filters, but it also weakens the structure of the paper element - hence I do it but don't recommend it. So far as foam pre-filters are concerned, the effect of oiling depends on the density of the foam. The rather low density urethane foam used in Briggs foam filters, and most Honda pre-filters, will not remove very much dirt from the incoming air unless it is oiled. If you just want it to filter twigs and chook feathers, don't oil it. You will, of course, then have to replace the paper filter fairly often because it will become fouled with various wet and dry contaminants, and only dry dust can be removed from it. If you oil the foam prefilter, it will stop nearly all of the dust, and even more of the oily exhaust, and you will wash it whenever it appears dirty, then put it back into service. The paper filter will last more or less forever if you do that. Being a cheapskate, I prefer that system myself. On the other hand if you are cursed with a higher-density foam pre-filter and you oil it, you may find that your engine cannot get access to much air, and it will run as if the choke were closed all the time. The solution is to procure a proper dry paper filter with a detachable low-density foam pre-filter, oil the prefilter, and clean the pre-filter as often as necessary. Of course you also inspect the paper filter each time, and blow it out from the inside with low pressure air if it gets grubby.
