Parasite transmission can occur from frozen rodents, as normal freezing doesn't necessarily kill parasite eggs. (example source)
That could be a roundworm, but hard to say sometimes even up close. The goopy stuff might just be mucus. The yellow dots remind me of Leucocoprinus birnbaumii, a very common fungus in herp enclosures (the yellow dots of that fungus are a distinctive part of the mycelium), which could have been ingested accidentally or may have been on the substrate where the goop landed.
Unless it is obvious one way or the other from an up-close inspection, I'd personally run that into the vet to get their input on the long white thing (and possibly include a fecal sample if one was available).
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