Squares of $F_{467}$ and 7 as a quadratic residue of a prime mod that prime

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I am having a hard time understanding what exactly is meant by this question. Could someone give me a solution with a clear explanation?

If $x=467$, are 111 127 and 225 squares in $F_x$? Explain your answer without using prime factorizations.

For what primes q, is 7 a quadratic residue modulus q? (The answer should be in terms of a set of congruence conditions on q)