I wouldn't worry too much about the black liquid coming out your exhaust. Does your bike sit outside, if so, does the cover pull all the way over the end of the silencers. With the amount of rain and wind lately, it's probably just water mixed with carbon soot (unless of course you have actually checked it and it is oil)
Re: The back wheel.
Assuming it is a drum brake, .You need to check the brake is not locked on. Firstly check the pedal moves up and down freely and then look at the brake pivot at the rear wheel/brake plate. You may need to take the wheel off, remove the shoes and pivot. Clean up the pivot with degreaser and fine steel wool, then something like copaslip on it before reassembly
If it is a disk brake, then you'll need to check the piston is retracting in the caliper. Over the winter this will attract a load of crud and could cause some corrosion thus preventing the piston from releasing. You can buy an overhaul kit which will include new seals.
It may also be the master cylinder again you can buy an overhaul kit for that.
Either way, you are only talking a few hours work with minimum outlay (none if it is a drum brake)