First it is a four stroke engine. Running two stroke fuel/oil mix will foul the spark plug eventually. That is all the “harm” it will do. I have been known to use my chainsaw fuel/oil mix in my four stroke lawnmower when I run out of mower gas.
For inexperienced folks like yourself, I recommend buying a service manual for the engine at least. It will have instructions on these kinds of procedures. I still use one after 50 years working on these engines.
To get it to start, we need three things; compression, fuel/air mix, (in the right ratio), & spark, (at the right time).
If it spins very freely when the rope is pulled, you do not have compression. If the rope pulls with obvious pulses of resistance, it will have enough compression to start. If no compression, a deeper dive is needed. Stop & fix this. It could be the valves, +/or a hole in the piston.
If the compression is good, & if the spark plug is new, we need to check for spark. Get a fire extinguisher & keep it handy. Remove the big wire from the spark plug & using an insulated pair of pliers, hold the wire 1/4" away from the engine. Set the throttle to idle, really any setting that is not the stop setting will work. While a friend pulls the rope quickly, watch for a spark between the wire & the engine block. The spark should be bright blue. If it is not, you will need to file the points. That is very doable but I will not go into that at this time.
If you have spark, pull the air cleaner off of the carburetor & shoot a small, 2-3 second squirt of starting fluid down the carburetor, leave the air cleaner off for now. Next pull the rope with the throttle set at or above idle. If it starts, or tries to start, the carburetor is most likely dirty & will need cleaned. However, first check for a full tank of good fuel. These engines start easier with a full tank.
Before you pull the carburetor apart, remove the tank & the carburetor as a unit from the engine block. Be sure to watch how the linkage for the carburetor is hooked to the governor so you can reinstall it correctly. This makes it easy to drain the fuel from the tank. Empty the tank & flush it out with known good gas. Reinstall the assembly, fill the tank, & try starting it again If it does not start, try the starting fluid again. If it still runs, or at least pops on starting fluid, but not without it, You get to disassemble & clean the carburetor. Buy a carburetor kit for your carburetor. It will have all the parts you need for this. It will probably have a few extra parts, as the kit is for several different carburetors. No worries, one can always use a few extra parts.
Let us know how this goes please.
IHTH, 48.