The second question is very similar to this question of Igor Belegradekthis question of Igor Belegradek.
Hempel's argument is still the only known one. It's the 'obvious' way to prove residual finiteness using geometrisation. To see how hard it would be to prove residual finiteness without geometrisation, imagine trying to prove the following much weaker statement with your bare hands:
Every non-simply connected 3-manifold has a proper finite-sheeted covering space.
