Is it permissible to eat spiced vegetables or pastries prepared by Chinese people in their company if we believe them to be free of pork oil, and are their hands and utensils ritually impure?

It is permissible to eat the food of non-Muslims if it is free from impurities and forbidden things, for the default status of things is permissibility unless prohibition is proven. The utensils and bodies of non-Muslims are pure unless their impurity is known. If their impurity is known, they should be washed. This is indicated by the fact that the Prophet performed ablution from a water-skin belonging to a polytheist woman. Moreover, a human being does not become impure by death, whether Muslim or non-Muslim.