Can anyone identify this microorganism?
They seem to be rotifers, the fuzzy (supposedly rotating) mouthparts are part of what convinces me. The behavior you mentioned of latching on the moss with their 'tails' is also a characteristic behavior of rotifers. They are also able to retract their bodies just as you mentioned.
Here are some images of rotifers that might support the argument.



I am least certain about the last image but I am making the assumption for now that it is either some variety of circular/retracted rotifer or a completely different kind of microorganism.
Stay curios!