This is a late responds, but never signed up any earlier. But I think you did get the Planaria for worms, I had some in one of my little tanks, because my fish was used to floating pellets and I had to feed him sinking ones, he got confused and I think I completely overfed, so there they started to jiggle on my glass. Buyt since I had plenty more tanks I just tookt the fish out, and didn't feed anymore, and then did waterchanges, cause I didn't want to lose the cycled water. With every water change I had less and less worm wigglers on my windows.
I think I have only put chemicals in my tanks for the first little while, and then stopped when I didn't see a difference in not doing it anymore.
Anyhow, I think in your case it is totally possible that they were stuck on something, may be gravel, or your Plants, I mean it takes what like two little mini things to infest your Tank right?
I think a good practice to do before putting anything in a tank is to boil everything before, get every bacteria off. Like who knows, maybe someone bought something after they had it in their Tank, and then returned it and shwoops there you go , you got infested with some weirdness.
This is the only thing I could think of that happened in your case, since you are not feeding anything, maybe some food from he previous owner got stuck in your plants, and never got removed form the plants, and TATA Wormlers here we are!
The slime, hmm, not so sure, may be it is algea from the light? Like sunlight. If you don't have any hair algea heaters in your Tank then you might get that. But I could not be sure, just a suggestion.
Well I know I was late. But may be it will halp anyway.
Take care for now.
Sarah1