The "parasites" may be snail parasites or perhaps just planaria that happened to be driving across the snails. Snails do have parasites, often ones that are specific to snails. In fact, probably a majority of snails have some sort of parasite, often intestinal worms. In most cases, they can live with those worms. Sometimes they may overwhelm the snail and kill it. The problem with medications is that most parasite-killing medicines also kill snails! So, there's a risk in using them. If you can find one that says it kills worms and specifically says it does not harm snails, then you could try that with no guarantees. If what you saw is a snail parasite, it most likely is not one that would also feed on the frog. They are usually species-specific.
The shell degradation may be due to having water that's low in pH or hardness. Have you tested the pH and hardness? You can add chemicals to the water to increase the pH and hardness or add in natural calcium sources such as cuttlebone or oyster shells in a mesh bag. My page on snails at
http://www.fishpondinfo.com/snail.htm has more on shell degradation. If the increase in pH and/or hardness is not significant, it shouldn't bother the frog.
A tiny 1.5 gallon tank is not really good for the African dwarf frog long term. They also like to have others of their kind. As Tommy said, they also need warm water (75 to 80 degrees F is good) so if it goes below 70 degrees F or so, the little guy may not do well.