An oven is a thermally insulated chamber used for the heating, baking, or drying of a substance, and most commonly used for cooking. Kilns and furnaces are special-purpose ovens used in pottery and metalworking, respectively.
In these mentioned cases, cross-contamination with najasah would make the food najis as well, and therefore haram to eat.
Unless you know that the common process in these restaurants is that they wash the pizza pan, change gloves, wash the knife, and so on. You can ask them these questions, and you can ask that the pizza not be cut, to avoid contamination from najasah.
As for using the same oven, that would not be a problem, because the pizza is put on a pan and then in the oven. If a pan is not used, then this is when there would be a problem.
In regards to french fries, or "chips", not only must the oil itself be halal, it must not have been used for cooking anything non-halal that is najis.
The oil must not be animal based, so it should be vegetable oil. What is cooked in it must not be najis, like meat that has not been Islamically slaughtered. However, if it is not halal to eat, but tahir, then there would not be a problem, like non-halal sea food. This is something you will experience in a fish and chips shop, where they might cook fish that does not have scales, or maybe even crab, in the same oil as the chips, or halal fish. In this case there is no problem, as long as there are no pieces of that food sticking to the food that you are going to eat.
And Allah knows best.