I think the thrust calculator is really useful thing. They even went to space with non-cup engineering using only computational methods and not a single wind tunnel test of SpaceShip One. Propeller must be a joke when compared to that.

EagleOne- every airfoil has a zero lift angle of attack. It is zero for symmetrical and negative for positively cambered profile. You can define absolute angle of attack so that zero lift occurs at zero angle.
But even prop with positive camber will work as windmill at high enough speed. Pitch times rpm may be not the most accurate way to estimate zero thrust speed, but as first approximation it should be fine.

Some props are not constant pitch props- pitch at tip is different from the middle and near the hub. For reason that such prop loses some top performance but have wider usable speed range. For example, if you have high pitch prop you may not be able to take off- when static, blade will be stalled at high rpm and no enough thrust at lower rpm to get moving, but decrease the pitch at some part of blade and voila- you are in the air.

I guess the zero thrust speed of propeller at given rpm (which comes from the limit of engine) is always higher than maximal speed of aeroplane in level flight (you may dive to gain speed). It may not be interesting to know this speed but for sure it does exist for every propeller at given rpm value.
The maximum speed of whole aeroplane in level flight is where thrust vs speed curve of prop-engine intersects the drag vs speed curve of airoplane. Thrust=drag. There is no eggs here. Better not to solve it analytically, graphic method is good enough.