In between freezings it is wisest to cook it. So if you take out raw meat, and then cook it, you can freeze it again. If you take out cooked stuff, you should get it piping hot throughout, cool it quickly, and then freeze it again. It may not have a super pleasant texture - if you don't ave an emotional attachment to it, you might want to just toss it.
I've looked through a number of recipes, and the vast majority of them indicate that you should cook the morels thoroughly (preferably in butter) first, before using them as a pizza topping or in an omelet.
I did find at least one recipe for a morel omelet that did not call for pre-cooking the mushrooms, however.
I must admit that I did my research a bit late, as I had already decided to risk it and made an omelet with morels, as I had not yet received any answers to my question.
I added the morels to the raw egg, rather than putting them in as a last-minute filling just prior to folding the omelet, so they did cook a bit during the process. The result was actually quite delicious (I also used some fresh garlic, chives, and Gruyere cheese), and I did not become ill.
However, it does seem that some people react differently, and alcohol consumption can greatly enhance any negative reactions to wild mushrooms.
Given the information I found on the Internet (none of it terribly authoritative, as the vast majority of quality information was on small sites maintained by wild mushroom hunting clubs and enthusiasts), I would not repeat my omelet without pre-cooking the mushrooms, nor will I make pizza without pre-cooking them.
The consensus seems to be that they should be sauteed once until "thoroughly cooked". At least one site (amid heavy cautions) specifies that this is usually 8-10 minutes, although I suspect that this is for intact mushroom halves, rather than small pieces (morels should always be sliced lengthwise to ensure that you can remove all the insects from the hollow center).
It needs to be stressed that even with the proper cooking, it seems some people have strong reactions to wild mushrooms, so use caution and moderation when trying them for the first time, and do not try them with any form of alcohol until you are sure that you can eat them without problems.
Best Answer
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.