Would I be allowed to prepare my laining on Shabbos for a parsha in several weeks from when I’m preparing? Similarly, would I be allowed to go over my laining for second day Shavuos on first day?
It is permitted to prepare the laining from Shabbos to Yom Tov, or from one day to the next. The reason is because right now that you have it prepared, it is considered as if you are right no a better person, because you right now have this knowledge, therefore it isn’t considered preparing for the next Shabbos.
Shemiras Shabbos Khilchoso 28 ftnt. 220, in the name of R’ S. Z. Auerbach zt”l. This would not necessarily permit studying for a secular test, as the actual knowledge is considered as important