"Dawn" (or "dawn on") doesn't mean "understanding," but rather "the beginning of understanding." It is similar in meaning to "epiphany" or "revelation." It is a metaphor for the moment the sun rises above the horizon and the light shines on your face.
I was trying to understand it for a long time and today it dawned on me: it is all about the cats. (I suddenly realized that cats were the key to understanding.)
Doesn't really work with this usage. Better to simply say "until I get it" or "until I understand the material."
Doesn't work. Try: "I don't get it." or "I am struggling to understand."