i'll answer your brake problem with, what i believe to be your solution, and then read the rest of your post.
new pads would probably fix your problem, but i don't think that you have to do that just yet.
there is a spring between the brake lever and the cup that the cable casing rides in. i'll bet you that if you chop that spring and remove about 1/3 of it, it will allow the lever to move the needed distance to get you the "contact" between the pads and the drum. i think your spring is collapsed and won't allow the lever to move far enough.