I have a few things you can check.

It seems you have two problems; a fuel line related one and a muffler related one.

Muffler:
The bubbles you see are most likely oil that comes from the exhaust. They could be a sign that the pressure nipple on the muffler is leaking. Some (most?) nipples has a nut on the outside of the muffler that you can tighten. If not you could try heat-resistant glue or liquid gasket material.

There is a long bolt inside the muffler. Loosen the nut (rear end), tighten the screw (front end) and retighten the nut. The rear part of the muffler has threads that the bolt screws into, and the nut is just a locknut. Black oil is usually a sign of metal-to-metal vibration.

The slime on the bottom of the silencer is most likely oil and nothing to worry about. The amount of oil depends of what type of fuel you run and how the engine was run the last few seconds before it was shut down. Full throttle means more airspeed through the muffler, and less oil is left inside. You can see this "phenomenon" if you let it idle for while (minute or two) and give full throttle.

Bubbles in fuel line:
This is not good. It sounds like you have an air leak somewhere. It doesn't take a visible hole to cause a leak, some times you'll only see the hole if you take the fuel line off and stretch it. A general rule of thumb: If the problems are there regardless of fuel level in the tank, the problem is most likely on the fuel line between the tank and the engine. If the problems appear at half tank or below, the problem is usually the fuel line inside the tank or the tank cap. I would retighten the cap and check/replace the fuel line.

This is what I'd do.