Does King's Edict choose units? Is it vulnerable to Not So Fast?

No, King's Edict does not choose units, and it is not vulnerable to Not So Fast.

Why King's Edict does not choose units

According to RiftJudge FAQ #509 and #322, King's Edict does not target or choose any units itself. Instead, the spell instructs each opponent to make a choice during its resolution. Because the spell itself does not perform the choosing, it does not "choose" a unit in the way that would trigger targeting restrictions or protections.

Why it is not vulnerable to Not So Fast

Not So Fast is a reaction that can only counter an enemy spell or ability that chooses a friendly unit or gear (FAQ #62).

Since King's Edict does not choose any units—and the choices are made by the players during resolution rather than by the spell itself—it does not meet the criteria for Not So Fast to target it. As noted in FAQ #8616, player choices made during the resolution of a spell are distinct from the spell itself doing the choosing.