I understand how positive dihedral helps dynamic stability in
airplanes, but some big ones, like the Russian An 124 Condor, has a
pronounced negative dihedral -- the wings have a noticeable downward
slope.

Q1: Do those airplanes need active fly by wire controls to maintain
stability, or is something else at play that keeps them right side up?

Q2: Does anyone have a design rationalization for such a
configuration, as opposed to just zero dihedral? I can appreciate why
fighters have it -- they exploit lack of aerodynamic stability for
rapid maneuvers -- but transports that spend their whole life being
straight and level are another issue.

Note: I have not morphed into an Mx clone!