For 2), you need to know that if p is an integer prime of the form 4k+3 then it is also a Gaussian prime. If it is of the form 4k+1 then it is always possible to express it as a sum of two squares, . Then p factorises in the Gaussian integers as , and those factors are both Gaussian primes. Finally, 2 factorises in the same way, .
So for example 11 is a Gaussian prime, but .