i'm not sure that i got this right, so it'll be nice to compare/certify with someone who did it.
a)
i think it'll take 2T and 2S. because it says that breaking is not equal to factorization of m. so C2 is just a regular number, because there exist a number n such that (n = e1+e2) and therefore C2 = p1^n.
similarly with C and e3+e4.
so it takes 2T and 2S because: 1 (each) for breaking C2 and one for breaking C.
b)
if i'm right, than the answer is "YES": all he needs is one key mod m1 and one key mod m3.
CORRECT ME IF I'M WRONG! THANKS!