I found a forum with other songs/rhymes:
Forum tik-tak.pl (for parents)
look especially at the second post (by Sosna) in that thread.
Some are simply short poems for children, but many of them are rhymes that accompany different games/plays (you usually have a description of different movements in the brackets).
warzyła sroczka kaszke, warzyła,
aż się w paluszek sparzyła,
temu dała na łyżeczkę,
temu dała na miseczkę
that's one of many versions
of this rhyme, you have a magpie here (instead of a hen) and there's no ripping off the head, but the middle part is very close to what I knew.