How do I know if escargot is fully cooked?
By the time escargot1 are heated to serve (I presume you had the standard garlic / herb butter gratin version served in the shell?), they have already been cooked for two to three hours in total. 

Escargot are killed by dumping them in their shells in boiling water, not unlike some cooks prepare lobster.2 

The soft body is removed from the shell, inedible parts and mucus removed, then cooked for another two hours. Snails will always be a bit chewy (they loose about 2/3 of their weight during cooking), but shouldn't be rubbery. 

After that, the meat is ready to serve or to be used in other recipes, stuffing them back in their shells with garlic butter is only one of them.

Without pictures, it's hard to tell what you mean by "black bits", from pigments in the snail's skin to flecks of herbs or peppercorns there are many options.



1  Typical cultivated species:

The Burgundy snail (Helix pomatia)

The Garden snail (Cornu aspersum)

2 Yes, some kill lobster before boiling them, but that's not the main topic here.