CB200T Oil leak, Carb leak, Spark plug wire gummed up

Hey so i'm new to riding and am really just learning about bikes, limited knowledge.
I'm just going to lay out all my issues in case one may be the cause of another.
Got the bike two months ago.
Was running great, always store the bike of the side stand and started noticing a slow leak each morning from my right carb overflow tube. After a couple weeks a noticed when using electric start (kick start is non functioning due to previous owners adding wide exhausts) she would start fine then the rpm's would drop and she would die unless I held the throttle open till she would keep running.
Next we got a heavy down pour and the bike wouldn't start. Had to boost her off a car which worked, but wouldn't start the next day until I gave the battery a full charge.
I also started to notice a slow oil leak which drips down onto the fins on the left side, it's been hard to trace but I think it may be from the gasket at the very top...
Had a poke around with a buddy, took the bottom of the leaky carb off and pushed (forgive my limited carb knowledge) a pin of some sort up a bit in hopes that we could decrease the amount of fuel. At the same time we had a look at my spark plugs. Had never changed one in my life before, that same right side the plug was totally black...Running to rich? When I rode home from his place the bike started misfiring on that right side. I stopped road side and pulled the plug cap off and the cap came right off the wire. This is how I discovered that the wire casing was dissolving and the end of the wires and the screw in the cap were gummed right up. cleaned it out and it got me home.
Changed the plugs last week and she ran great, no more issues when starting. That only lasted a couple days (and my ride to work is less than 15 minutes) and she started to gum up and misfire again. Here's picks. Could oil be leaking down my wires and causing this? Should I be replacing the wires? I don't think the whole ignition coil needs replaced just the wires, but i'm not really sure what the wires should look like at the end that attaches to the cap but it's probably not this.
Also could this black plug issue mean I need to adjust the carb on the right side/both?
Thanks a ton for any feedback!