Is it permissible to learn different permissible worldly skills/education from non Muslim? Is it imitating them? And can a Muslim also teach these to non Muslims?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is nothing wrong for a Muslim to teach a non-Muslim worldly knowledge (sciences). Also, there is nothing wrong with a Muslim learning worldly sciences at the hand of a non-Muslim; this has nothing to do with the issue of imitating them.

The children of the companions learned writing from the prisoners of the Battle of Badr.

Ibn Abbaas said: “There were people among the captives on the day of Badr who did not have what to ransom themselves with, so the Messenger of Allah made their ransom to be teaching writing to the children of the Ansaar.” [Musnad Ahmad 4/92] [Al-Arna’oot graded it as Hasan]

Allah Knows best.