Why is subsonic lift at 25% of chord?
Lift isn't at 25% of chord, the aerodynamic center is. Lift acts at the center of pressure, which depends on the wing's camber and angle of attack.

Broadly speaking, you can split lift into two constituents, one from camber and one from angle of attack. Deploying the flaps on the Dash-7 changes both camber and wing chord, and of course shifts the center of pressure back.

Changing the angle of attack will add a pressure change over chord which has its center at the quarter chord. The reason has to do with the strong local curvature near the leading edge which causes strong suction peaks. For a more mathematical explanation see the work of Birnbaum. Or read this answer.