What is the relation between the Lift Coefficient and the Angle of Attack?
Normally the relation is linear within the practical range of angles of attack used in flight. However, the Mach number and the Reynolds number will cause shifts. For the Mach effect, use the Prandtl-Glauert rule in subsonic flow up to Mach 0.7: $$(\alpha - \alpha_0)_{Mach} = (\alpha - \alpha_0)_{incompressible}\cdot\sqrt{1-Mach^2}$$

A higher Reynolds number means a relatively thinner boundary layer, and since the boundary layer on the suction side of the airfoil grows in thickness with increasing angle of attack, the same airfoil will have less boundary layer growth at a higher Reynolds number. This translates into a higher effective angle of attack at the same geometrical angle, so the lift curve slope becomes steeper and will reach stall at a higher angle.

There are no standard conditions, but a proper lift curve graph should note both the Mach and Reynolds number for which it is valid.