The question Fields and proper subfields., which asks if a field can be isomorphic to a proper subfield was closed as a duplicate of Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$.
Ofcourse, (the answer to) the second question answers the first, but I don't think this should be considered a duplicate (at least not of the second one). In particular, someone coming up with this question when starting to study fields, might not even recognize that the second question gives an answer.
Edit: I realize that the general question in the title is likely unanswerable (other than "maybe; depends on the questions"). My concern is actually with the specific questions.