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Yes, those rules are important to know. The first two will help you answer if the reaction is product or reactant favored, and the last three will help you answer/determine which direction the reaction will proceed. It would be hard to answer these sort of questions without the rules.
I definitely think that memorizing those rules is the best way to go because it's hard to know which reaction is being favored without them if you are given concentrations/partial pressures for both products and reactants in a problem. The way that I remember them is actually the opposite of how Lavelle teaches them, I find it easier to remember it as when K > Q, K < Q, and K = Q because if you order it this way then your <, > signs point to the direction that the reaction is going. If this confuses you then just stick to Lavelle's way but I found it easier to remember.
You can memorize the rules but I think it is also good to understand why the rules are the way they are. If you think of K and Q as ratios and know that Q will be moving towards being equal to K then it's not necessary to memorize the rules. If Q is smaller than K its because the denominator (reactants) is bigger and the numerator (products) is smaller so then the reaction would favor the products in order to increase the value of Q to match K. If Q is bigger than K it's because the denominator is smaller and the numerator is bigger so the reaction would favor the reactants to decrease the value of Q.
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