some questions about permutation

question 1: if f and g are both one-way trapdoor permutation with the
same domain and range. Is it definitely to say f*g = g*f ?


question 2: if f is a psedurandom permutation family. Is it possible to
find such k1,k2 and k3, satisfying f_k1(f_k2) = f_k3? or f_k1(f_k2)=
f_k2(f_k1)?

question 3: We know m^a = m^b mod N will leak some factor information
for phi(N), so for some deliberately chosen m, is it helpful for
factoring problem?

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