Is it necessary to "heal" clay pots?
TL;DR: You should.
I don't own clay pots myself, so take this with a grain of salt. I found some information on the Bram Cookware website called Clay Cooking 101. It has recommendations as well as an instructional video.
The process apparently is called seasoning, rather than healing. Here is a short summary from the page:

Seasoning Your Clay Pot
Give your new clay pot love and it will love you back! Cookware that
will be used over a direct heat source on the stovetop needs to be
seasoned before its first use. This strengthens the pot and prevents
it from cracking. It will also make the pot more durable so it can
provide you with many years of fantastic cooking.

Now for the black particles in the food, I'm not certain what that could be; so it's probably best to play it safe and not eat the food.