I did a re-ring of my GCV-160 last year. I ran into the same issue with the blade adapter, wd40 just won’t cut it, you’ll need something like kroil oil or liquid wrench and heat. I recommend taking the bolt that holds the blade adapter on to the hardware store to get some grade 8 bolts of that size in various lengths. I had damaged the head of the factory bolt and bent a lower grade bolt in my attempt to get it off. You’ll need the various lengths because once you get it loss, it’ll still not just come off, you’ll need the different length bolts to continue to use the jaw puller. I had put both blades on the blade adapter very tight to keep from damaging the blade adapter, then used a two-jaw puller to grasp the edges of the blades with the center drive rod on the blade adapter bolt. It took me multiple attempts over several days to get it off.
As for the rebuild, a great set of videos to watch
https://www.youtube.com/watch?v=-B-H5tgxd7E . Most people will say that your foolish for rebuilding a throw away engine, but if you have the tools, and don’t spend to much on shop supplies it won’t be to bad. It cost me about $45 to do a re-ring with all new seals, o rings, timing belt, gaskets, GCV190 cast valve cover, and three broken bolts. Add another $30 to that if you need a new crankshaft. If the cylinder ($50) and crankshaft ($30) are both bad, then you might want to look into getting a pulled GCV190 from a pressure washer on ebay for around $110, then just put in the correct crankshaft for the lawnmower, and carb linkages from the GCV160. Don’t try to take the muffler off the engine, I broke both bolts in my attempt to get it off, an impact wrench is your only hope of getting it off. Clean the combustion chamber and valves good when you have it apart, I used MOPAR combustion chamber cleaner with great results.