Why does electron flow from anode?
The semi-reaction of reduction for Zn is :

$Zn^{2+} +2e^- \rightarrow  Zn \quad E^\circ =-0.763$ 

The semi-reaction of reduction for Cu is :

$Cu^{2+} +2e^- \rightarrow  Cu \quad E^\circ= 0.337$ 

The standard redox potential for Cu is more positive thus it is reduced and Zn is oxidized.
Electrons flow from a negative to a positive potential. They flow towards the cathode because their potential V, at the anode is more negative, thus they have an higher potential energy: $U_e = V*e$

note that $e$ the charge of the electron is negative as well as V.