What is the ruling on eating from restaurants that serve pork, given that the order does not contain any meat, and is it permissible to eat a pizza that does not contain meat or prohibited ingredients from a restaurant that serves pork?

There is no objection to buying and eating non-forbidden foods from a restaurant that serves pork, unless the utensils and dishes used to prepare the permissible food are contaminated with pork or other impurities. If you know, or it is highly probable, that the food is prepared with contaminated utensils without them being washed, then it is not permissible to eat it. However, if the utensils are different or have been washed, then there is no objection.