Hi Peter, to get the engine size I suggest you start with the engine type, which is cast into the crankcase. See owner manual:
http://www.ronebergcairns.com/2010onwards/general2010_5844.pdf
Valve clearances for the GXV160 are 0.006" inlet, 0.008" exhaust, which is the same as the GXV120 and GXV140, so from that point of view it doesn't matter which capacity the engine is.
The Huayi, Ruixing, and another brand I can't recall at the moment, carburetors are all close copies of the Keihin, and generally speaking the parts are interchangeable.

In my experience it takes a while for a Honda with new rings, to dirty its oil. However as you say, half-a-dozen mows of an average suburban lawn would have it discoloured, though not non-transparent. To have a dirty air cleaner in the same amount of time does sound strange - maybe it had been run more than you think, and the oil had been changed. Incidentally the owner manual I've directed you to has some detail on caring for the air cleaner. Please post a picture of the inside to show how dirty it was and where the dirt was located. Did it have the foam prefilter fitted, and was it oiled?