Every time I make a cut using Boolean it leaves behind extra geometry like the thing I circled in blue, I have to manually delete those faces to have a see through cut, why is it doing that??
because boolean is crap, and should never be used 
also, i cant see any trouble with the images, try to show the wires so we can actually see what ur talking about.
Edit: found the issue! For Boolean to work properly the object being cut has to be 4 sided not just a 1 sided plane, I had to solidify the object for it to work right.