Just wanted to clarify, "imply" = something that must be true but not stated in the passage. Is this correct? So if the question asks " The 3rd paragraph implies the message that..."? Are the hidden assumptions for the arguments in the passage the correct answers?

Hi Abhi. To 'imply' means to suggest implicitly, instead of explicitly stating something. Let me clarify using an example:
The author says: 'A new education policy should be implemented as soon as possible'. Here the author implies that the current education policy is not working/could be improved. Though he does not say that explicitly since he is advocating for a change urgently, it suggests the state of the current policy.
Assumption is something that bridges the gap between statements and conclusions:
Example: "All students who are not good at studies would be happy if the exams are scrapped. Therefore, Kartik should be happy that the exams are scrapped". The statement here is that the scrapping of exams would make average students happy, and the conclusion is that Kartik is happy. The gap would be bridged only if we assume that Kartik is not good at studies. Because if Kartik were a topper, the conclusion would stop making sense.
Thus, to answer your question, it is not necessarily so. To see what the author is implying, look at what he/she is subtly hinting at. To find what the hidden assumption is, look at what additional piece of information if added would make the author's conclusion more sensible. Hope this helps.

Thanks !