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I know my hikari frozen food say's to be assured to have no parasites or contamination, so I'm confident it doesn't, and if it does, you can report it to them and they can somewhat compensate you, but I never had issues either with frozen food. BloodWorms, Krill, BrineShrimp and BeefHearts is what I use.
They certainly can, especially with bloodworms since they have a exoskeleton that is hard to digest and process and could potentially get stuck in the intestinal tracks irritating the walls allowing flagellated protazoas to take hold causing digestive issues. I don't feed any frozen foods or supplement anything else but NLS.
freeze dried is safe because the parasites can not survive in the dried out state, however frozen they can, freezing does not kill the parasites, though most companys like hikari treat the food other ways to kill parasites, though the risk is always their when it comes to frozen foods.