Hi Kmikaeli,
Let's see if we can help out here. One of the issues is that you are mixing a lot of ideas together, so let's separate some of that out first
Errors of assumption occur constantly on the LSAT, and as will be explored in more detail in a later chapter, an assumption doesn't always mean that you assumed something
was the case; in many instances, assumptions revolve around assuming something is
not the case. So, for example, Improper Comparison answers assume that the two items are essentially similar
and that no relevant differences occur. The conclusion then makes a judgment based on that mistaken assumption, and the correct weakening answer often points out this problem. Incomplete Information answers assume that the author had all the accurate or relevant data and that no important data was missing, and then make a similarly flawed conclusion. However, the three types there are just broad ideas to get you thinking—they aren't the only three types of Weakening answers in existence. That said, I do have a suggestion given the questions you posted, and that is that it might actually be worth your while to jump ahead to Chapters 11 (Assumption) and 15 (Flaw in the Reasoning) and scan through those (there will be elements from interim chapters that you won't have seen yet, but just bypass that stuff for now in the interests of getting a bigger picture view of these ideas).
With truth and validity, let's go back and look at the comments I made there, because I think that may help here. I'll add some italics as well to help clarify. I said, "When we evaluate LSAT arguments, we are
primarily concerned with validity. That is, what is the logical relationship of the pieces of the argument and how well do the premises, if accepted, prove the conclusion? We are less concerned with the absolute, real world truthfulness of either the premises or the conclusion...In most cases, the LSAT makers will let you work under a framework where the premises are simply accepted as factually accurate, and then you must focus solely on the method used to reach the conclusion.
In a sense this could be called relative truthfulness—you are only concerned about whether the conclusion is true relative to the premises, not whether the conclusion is true in an absolute, real world sense."
You might be able to tell I'm walking a fine line there—"truth" is an issue of some significance in the logical/philosophical realm, but at the same time I didn't want to get too deeply into it since it's not as important in the LSAT world. With that in mind, the statement that "If the premises are accepted, how well do they prove the conclusion?" is built around how that works from a logically valid standpoint. Depending on how you define truth (using a real world or philosophical definition changes things), you can say that truth plays a role, but I would say don't get caught up in worrying about the definition. Instead, ask yourself if the conclusion makes sense or if it is proven by the given premises. That will typically do the trick, especially because the LSAT itself won't get into the "truth" issue.
Please let me know if that helps. Thanks!