You prove (a) by induction. First show that it is true for n=1 and n=2, then show that if it is true for n=m-1 and n=m-2, then it must be true for n=m.
You also prove (b) by induction. It is trivially true for m=2. If it is true for some m, that is the statement "if f=gcd(Fm, Fm-1) and gcd(f,e)=1, then f|d" is true, then if f=gcd(Fm+1,Fm) and gcd(f,e)=1, f=gcd(cFm+eFm-1,Fm) and use the properties of gcd to show f=gcd(Fm, Fm-1) and therefore f|d. So the statement is true for m+1.
Post again in this thread if you're still having trouble.