[frogparty]

Yes you can. Wait a little longer till the pups are at least 1/3 the size of the mother plant, and snip the stolon with a sharp knife or scissors.

 

[frogparty]

yes, the stolon will become more apparent as the pups grow. cut near the base of the mother plant, not the pup.
The grey bugs...are they fluffy looking? like little bits of cotton? or are they springtails?

 

[frogparty]

if they are cottony its mealy bugs. Throw plant away. Mealy is, IMHO, the hardest pest insect to kill