you will need to use modular arithmetic for both of these questions.
for Q 1, you have to consider what all the squares are mod 3.
Q2 is about twin primes. In a pair of twin primes (other than 3 and 5), one is congruent to 5 (mod 6) and the other is congruent to 1 (mod 6). You have to consider what this implies about their 4th powers.