If I use a technique for shading that looks like this: https://shorturl.at/LLAW instead of using something like cel shading, would this be against the rules if my chosen colors are black and white and the color of the shading is still black or white?

Alpha is allowed, yes

you’re asking if hatching or cross-hatching is allowed and… does that create any more colors? it doesn’t look like it. all of the hatching in that image is done with the same color: black.