Basically, じゃないですか (or informally じゃないか? , じゃない?, or じゃん?) can be used in a similar fashion to a rising tone ね/でしょう/だろう (asking for confirmation).
[negative form] んですか meanwhile is asking for an explanation about the action in question. This can naturally sound accusatory or part of some rhetoric. Think “Did I not tell you to pick up milk yesterday!?” or “Is it not true that our political opponents have only maintained power through bribery and corruption?”
So in the first example, 夕食を食べないんですか has a ring of “Why are you not eating dinner” while 夕食を食べるんじゃないですか has a ring of “Weren’t you planning on eating dinner?”
Also, note we have a grammar question thread, which is more likely to be responded to.