Welcome to OCC! I love 82 series cubs, and it looks like the one you have is still in great original shape. I'd take it over that one next to it in a heartbeat
Just general background info for you:
You have a MTD built 782. IH stopped (and MTD started) building them in June of 81, so anything after that is MTD. It is almost identical to the IH built ones, except it likely has an aluminum rear end casting instead of a cast iron one that IH ones would have. That's not an awful thing at all, just make sure that the bolts that attach the frame to the rear casting are tight.
Please check out the tech section for the service manuals and operators manuals for it. They will have everything you'll ever need to know about your tractor in them.
The KT-17 II is the better of the two engines that these would have come with, so that's very good. It is a battery/points ignition just like the previous K series cubs. The ignition system is basically the same as those single cylinder ones, except the coil fires 2 plugs instead of 1.
If those are all original hours and the engine hasn't been touched, it's likely that engine is pretty worn out. That's pretty close to the max expected time between overhaul you'd expect out of a K series engine. I'd check compression and see what that looks like. The manual says a 10% difference between cylinders is a problem. It also says under 90PSI is a problem.
The KT-17 (and M18s) do tend to have fuel pump failures. Usually, when they fail, the membrane is what fails and you end up with gas going into your crankcase. This is the most likely fuel-related failure on these (other than the obvious carb problems with a engine that has sat for a while). Check the oil level and see what that looks (and maybe smells like). The fuel pump isn't hard to replace if that's what it is.
Also, listen to ol' George on these things. He's a wealth of knowledge on the Kohler horizontal twins.
Most of all, that tractor looks super well taken care of, considering it's 34 years old. A good bath, some wax, and a new seat and it'd look basically new!