OK so for 1 I know it's (n-1)! (because cycle 1234 is the same as 2341) but I don't know how to prove it

for 2a) we know that if cycle has c_{k}elements then it's sign is (-1)^{ck-1}and we know that sgn(a*b)=sgn(a)*sgn(b). Does the second equality mean that ? If no, how to prove it?

for 2b) we would have to prove that but I don't know how to prove it - help?