You can pop the reservoir off by either simply pulling it upwards or carefully prying with a suitable stick of wood between the two reservoir spigots. If the reservoir is tight in the seals, as it should be, this takes a bit of force, but be brave. The first time I did it, I had my heart in my mouth, thinking I was going to wreck something. My theory is that if the reservoir comes apart it was probably going to leak soon anyway. Once off, you can inspect the seals (they come out easily once the reservoir is off) for cracks and general disintegration and to check that are still reasonably pliable. Also inspect the orifices into the MC for debris or gunk. I use a large syringe to suck the MC as dry as possible before commencing and then to pull any remaining fluid, including grit, from the orifices.
AFAIK the sooty looking stuff is disintegrated rubber, presumably from the reservoir seals and maybe backwashing from the MC proper, although I don’t think this should happen.

Good luck,

--
Barry -- 1967 122S 'Betty'