Is it permissible for a Muslim to work in a slaughterhouse that slaughters sheep in a non-Sharia-compliant manner (stunning and piercing), and is it permissible for him to participate in cleaning and carrying them, and is prayer permissible in clothes stained with the blood of these sheep?

It is not permissible for a Muslim to work in a slaughterhouse that kills sheep by electric shock and does not slaughter them according to Islamic rites (tadhkiyah shar'iyah); this is because it involves assisting in what is unlawful, which is consuming carrion (maytah). It also involves destroying the animal and wasting its value. The Prophet, peace and blessings be upon him, forbade killing an animal by "sabran" (i.e., confining it and killing it slowly).