Is {3} a sub set of {3}?
Yes, AFAIK.
Does {3} = {{3}}?
No, {3} is an element of {{3}}.
Does 0 belong to the empty set?
Possibly No, but I am not sure.
Does 0 belong to the empty set inside a set?
This depends largely on the previous answer. So, my answer would be no. But again, I am not sure on this one too.