The wiring by the rev limiter needs to be fixed/connected together. That's the wiring for the ignition kill circuit so the engine shuts off when you take your foot off the pedal. Black wires connect together, and there should be a white with black stripe wire that meets those near the base of the oil fill/dipstick tube. Of course its possible there's some other redneck engineering going on in other places so if you connect those together and the engine doesn't run at all, then leave them disconnected temporarily and we can narrow down that issue later.
The carb probably needs to be removed and cleaned very thoroughly to fix the power issue. You shouldn't need a kit or any gaskets unless they've been damaged previously. If any gasket wan't to stay stuck to the carb just leave it on there. Remove the bowl, the float and needle, and the main jet. There's a pilot tube in the center of the carb above the main jet, use a screwdriver to reach into the venturi and push down on the top of the pilot tube and it should drop out with a few taps of the carb on the bench.
Clean all that and make sure all the holes are clean as well as the bowl vent port a the top of the carb.
Remove the idle pilot screw on the side (brass screw) and make sure the holes in that are clean, use cleaner and compressed air if you have it to make sure the supply openings for that are clean and make sure the idle mixture ports inside the carb bore are clean and you can see cleaner spraying out of them. The idle mixture screw is not removeable, but usually does not need any attention other than some cleaner and air blasted through. The mixture screw is supplied by the same ports as the idle pilot screw. When re-installing the pilot screw do not over tighten the screw or you can crush the screw and block the openings in the screw and in the carb.
Also, Thank You for being thorough in your post! The more details the better!
Many people post a single question and simply ask "why its broke?", as if we're magicians, and then we have to ask for more details anyway. Much appreciated to have most or all relevant info supplied up front!
Also, Welcome to the BGW!