what is the most important day of rush?

about your second questions, sororities will never make you put them before your grades, after all you're a student above all. if you have class or some other important school thing, ive never heard of sororities penalizing you for missing anything as long as you're telling the truth (missing mandatory things because class is fine, missing mandatory things because you didnt feel like going, not so much).
For the 1st, there is no "most important day", not really. treat every day like it's the most important in order to not get dropped. preference night is the most personal, if thats what you mean.
What you do during rush is, every day you go to visit houses, starting with all of them (split into two days), then you drop some and the sororities drop girls, and you go to less and less each day. so you'll start with going to 12 (if chi o participates), then 8, then 5, then 3, and then you run home on bid day to wherever you got your bid. it's a stressful week, i wont lie. it's hot an tiring and emotionally draining and chances are you'll cry at some point, due to stress or whatever. but the feeling of opening up your bid card at the end of the week (if you got a bid you actually like) and running home makes up for all the stress of the past week.