Why is the stagnation point on the upper surface before the start of circulation?
The illustrations under the time-invariant, inviscid, irrotational and incompressible (potential) description is a bit misleading, in my opinion. In the real world, assuming the airfoil starts from rest (no flow field) and you start accelerating it to some airspeed, viscosity should start generating vorticity as soon as airspeed becomes non-zero. Therefore, the non-lifting flow field would never exist in the first place.

The non-lifting flow field serves better as an illustration of the flow solution using uniform + doublet flows. In this case, there is a unique solution for a uniform flow past a cylinder with radius $R$:


Radial speed: $V_r=V_\infty cos\theta(1-\frac{R^2}{r^2})$
Tangential speed: $V_\theta=-V_\infty sin\theta(1+\frac{R^2}{r^2})$


Since we can conformally transform most airfoil geometries into a cylinder, flow solutions past a cylinder is a generalization to those past airfoils. The above result assumes zero angle of attack. But since cylinder is symmetrical, a non-zero AOA simply rotates the result by that AOA, and that's why you have the rear stagnation point on the upper airfoil surface.

For a lifting flow, we would need to model with uniform + doublet + vortex flows. In this case, a set of solutions can be obtained for a cylinder:


Radial speed: $V_r=V_\infty cos\theta(1-\frac{R^2}{r^2})$
Tangential speed: $V_\theta=-V_\infty sin\theta(1+\frac{R^2}{r^2})-\frac{\Gamma}{2\pi r}$


Notice that there is, at this point, no imposition on what the vortex strength ($\Gamma$) has to be. You can have an infinite number of lifting solutions with an arbitrary value of vortex strength (at the same AOA). I think that's what (b) and (c) of your second set of figures are trying to illustrate. We get around this by specifying the Kutta-Condition and impose the stagnation point at the trailing edge to get a unique solution.

Since the total flow field must have zero circulation, the starting vortex must have a counter-clockwise circulation.