6.5 is one of the most common types of small engines. Sorry to hear you didnt figure it out. I cant really help much but here is what is running through my head right now.
basically, engine needs
fuel
spark
air
most common problem is bad gas and a clogged carb, which doesnt give u much fuel. Could be a number of reasons, but if your engine runs poorly our out of wack, and you have spark, it could mean that your timing is off (almost exclusively caused by sheared flywheel key, you can pull the nut off with an impact wrench and make sure it isnt sheared).
not enough air would be an issue with the air filter, so if you run it with air filter vs without, you could weed it out. minor problems with air would be leaky gasket AFTER the carb (so carb to engine- making it run lean but based on your spark plug issue, almost sounds like it runs rich? If it runs super super rich you get lots of smoke and poor performance. Did you check the jet to see if it may have been tampered with?
My gut feeling judging from all the rust on that engines muffler and tank is that it has been out in the weather and is really old. Leaving an engine outside for such a long time can cause a lot of rust to happen, especially if it has a valve partially open when it is stored. You would need to 'test' for compression by taking off the flywheel cover and just turn it over by hand, you should really feel the flywheel want to bounce back fast as it is coming into the compression stroke as you turn it over. If you take the plug out, you will notice it spins freely, but with plug in it shoudl still spin freely until it starts building compression. If you still get it spinning freely as you rotate it by hand, you might have an issue there with valve seals and ring seals.... it just looks very worn out though so it could be other issues that you cant see and are not easily diagnosed.