Is it permissible to use a heater and a cooker belonging to an oppressive governmental health center, knowing that my uncle, who works at the center, brought them home claiming they were not needed and would be returned later? Is it permissible to eat food prepared on them? How do we repent for food previously consumed? Does this affect the acceptance of prayers?

The default rule is that it is not permissible to use work tools for purposes other than those for which they were designated, or to take them outside of work without permission. The mere fact that the ruling authority is oppressive does not permit taking its property unlawfully, unless a person has actually been wronged by it, in which case he is permitted to take an amount equivalent to his grievance, if that is the only way to obtain his right (the issue of al-Dhafr - obtaining one's right by force). You should denounce your uncle's and your mother's actions in a good manner. As for the food cooked with the aforementioned device, it is not forbidden to eat it; at most, it may be considered makrooh (disliked) by some scholars. If you refrain from eating it as a form of denouncing evil, then that is good.