Restaurant

Question

I have a few questions about your fascinating reply to Joe. 1.How can they grill vegetables for you in the restaurant -- isn't it bishul akum? 2. You say that if the restaurant is owned by a Jew or the chef is Jewish then there is no bishul akum problem. But if it's owned by a Jew and the chef isn't Jewish, why isn't it bishul akum? 3. How can you order vegetable soup? What about bishul akum? Also, since they are using the pots to cook all day, and some of these soups are non-kosher, can we stll say setam kelim einam benei yomam? 4. Re. cheeseless pizza, again, I am wondering abouit bishul akum (or is pizza not oleh al shulhan melakhim)? Also, why aren't we concerned that in the same pizza oven where they also cooked the pepperoni pizza, some of this pepperoni might have fallen onto the oven right underneath where the cheeseless pizza is now cooking, thus treifing up the cheeseless pizza. Thank you very much. I learn so much from this site.