Regarding level 4 comp, first I'd recommend checking out the Harry Potter examples they give for each level of comp in the detailed roadmap. Second, the piece of advice I've been given is that level 4 comp feels like you understand messages, but whenever you don't it's tough to pinpoint why. In level 3, you know you just couldn't hear it, or didn't know enough words, or were unfamiliar with a grammar point. In level 4, you'll feel like you should know most of the words and grammar used, but the meaning isn't coming to you like you expect it to and you won't know why.
As for monolingual dictionaries, go check out The Moe Way's dictionary drive. You can find it here:
https://learnjapanese.moe/yomichan/
There is a folder full of dictionaries, and in the main drive there are documents explaining the ins and outs of each one. I personally use the 旺文社国語辞典第十一版 as my top priority because the definitions are about as easy as monolingual can get, but I have the others downloaded for future reference as well.