I know that squid is often cooked for one-two minutes to make it still tender. However is one minute enough to kill possible parasites? What is the minimal time of boiling for squid? If that's important then lets say it's already cut into small rings. It's frozen but I am worried that freezing might be incorrect or not enough.
As is usually the case with food safety, it is not purely the time something is cooking, but the temperature. Most recipes, even for fresh squid, call for a very short boil in water. If, out of an abundance of caution, you wanted to make absolutely sure that your squid is cooked safely, the CDC mandates that the internal temperature of seafood should reach 145° F [~63° C].
The most cautious method available is measuring the internal temperature of your cooked squid to ensure that it is up to temperature. That is the most surefire, consistent way to test food safety.
However, this is probably overkill and is especially overkill if your squid are already frozen.