NACA profile calculations

I have got into plotting NACA profiles by computing. Humbly beginning
with the simplest, which I presume to be NACA 4-digit, I found the
Wikipedia page as a prime source of information.

Plotting a symmetrical profile is not that hard: at regular intervals
(=X along the chord), one calculates the thickness (=2*Y) and plots a
dot at X,+Y and another at X,-Y . The formula for the thickness is
netaly given in the wikipedia page, neat!

The first step of assymetrical is just as easy: draw the camber line by
calculating its offset from the chord at regular intervals. From the
camber line. intrados and extrados points are again a vector away; and
the magnitude of the vector is calculated in the same way. What beats me
however is that, if I interpret the wikipedia page correctly, this
vector should be considerd perpendicular to the camber line, where I
would expect it to be vertical, i.e. perpendicular to the chord.

Any comments here?
Is my understanding of the wikipedia page correct?
If so, what's a useable algorithm to plt intrados and extrados?

And also, less poignant but still:
How do I calculate from the basic parameters the behaviour of the
profile, i.e. the Cl curves? And perhaps other nice info like the
leading edge diameter?

Generally: any pointers to in-depth information that a non-engineer can
mentally digest?

TIA,