I crushed this game in my first go (4:00) and was pretty stoked about it, so allow me to share my method with you:
First, here's my initial diagram:
You'll notice a couple things that are different from a typical setup (ignore the Q21 and Q23 diagrams for now):
First, the red is what I visualize in the setup. I personally only feel it is necessary to diagram out actual slots when there is, for example, a fixed, unbalanced game (for example, 3/3/2). In this case, because they are all even, I can just accept this and not waste time for my hypotheticals. I can just write ORW and letters under it. Being comfortable with visualizing it in this way will already save you time when attacking the questions, but without the cost of accuracy.
Second, notice how I didn't create not-blocs, but instead created conditional statements. You can represent the symbols however you want, but a horizontal line with a / in the middle is quickest for me and is my own personal shorthand. Also notice that each conditional statement contains the blocs from rules 1 and 2 where applicable.
Third, notice how both rule 5 AND its contrapositive are expressly written. When you attack logic games, it's almost always worth writing out every contrapositive, and especially if there is only one.
Lastly, I star any variables whenever I notice they are unrestricted. Neither L nor N are ever mentioned in any of the rules, and therefore typically have much more freedom than the other variables, which are all constrained in some way. You don't need to do this initially, but any time I notice it, I make sure to star it.
Now, let's attack these questions.
For question 20, any time you see an initial question that says "Which of the following is an acceptable setup?" or something similar, it is always a check on whether or not you understand the rules. The best time to test whether you understand the rules is while you are initially diagramming. I almost always attack the answer choices AS I WRITE each rule. Doing so is the most efficient use of your time, as instead of jumping rules, you are introduced to AND apply the rule immediately, making it more concrete in your mind. With very few exceptions, I recommend doing this almost every chance you have. (Exceptions include highly conceptual setups that are more difficult to juggle in your mind collectively, and I can't offer an example.)
Question 21 is a single hypothetical question (see above). Given MP in W, K must be in W, and since P is not in O, H cannot be in O, so it is in R. FG cannot be with H, so it is placed in O, leaving L, N, J unrestricted. Answer choice A must be true and therefore you can circle it without bothering to read any of the other choices and just move on.
Question 22 is essentially a free question based on how well you diagrammed the initial rules and deductions. Glancing back at the conditionals and blocs we have, the wrong answers melt away in a few seconds leaving only C.
Question 23 is another quick, single hypothetical (see above). KP in R requires M also in R, and because P is not in O, H must be in R again, putting FG in O. Again, L, N, and J are unrestricted. Glancing at this diagram immediately rules out every choice except D.
Finally, Question 24 is also a free question if you wrote the first two rules as blocs of FG and KM, respectively. A is the correct answer because it mandates four variables in the same group, which violates the initial premise.
I hope this helps and best of luck!