Translation:The fresh meat is cooked with potatoes.
There is no "the" in the original sentence. The meaning is slightly different. "The potatoes" indicates specific potatoes." While just "potatoes" indicates the recipe the method of cooking or preparing the dish.
So you would use μαγειρεύεται if you wanted to know how something is cooked Πώς μαγειρεύεται το κοτόπουλο;
Correct. This is how you use the verb in the passive voice in Greek. Το κοτόπουλο is the subject of μαγειρεύεται. If you want to ask someone how they cook chicken, then you say Πώς μαγειρεύετε το κοτόπουλο; (Εσείς μαγειρεύετε το κοτόπουλο - S V O)