An assumption can be either true or false, but for LSAT purposes, it doesn’t really matter. “Logical reasoning” is, essentially, the ability to determine whether conclusions follow logically from premises, whether those premises are stated or unstated (assumed). For instance:
To get into law school, one must do well on the LSAT. Therefore, one needs to study in order to get into law school.
The argument takes for granted which of the following:
The answer, of course, going to be something like “It is necessary to study to do well on the LSAT.” It’s totally irrelevant to the question whether that unstated is “correct” as a matter of fact or not. It’s a “leap” in that it’s a necessary component of the argument – if it’s not true, the argument falls apart. But is it correct? It doesn’t really matter. What does matter is your ability to recognize it as a critical step between the stated premises and the conclusion.
I’m not sure exactly what you mean by your last question, but basically, assumption questions care about one of two things, depending on which type of assumption question it is –
1) In a sufficient assumption question, the assumption, IF IT’S TRUE, gets you to the conclusion.
2) In a necessary assumption, the absence assumption, would kill the argument. In other words, IF IT’S FALSE, the argument doesn’t work anymore. This is also true for “general assumption” questions, i.e. “The argument assumes which of the following”
Whether the statement is “actually” true or false doesn’t really matter; you’re always just analyzing them hypothetically. “If (B) is true, would that guarantee the conclusion?” or “If (D) were false, would that kill the argument?”
Note that on a sufficient assumption question, you don’t care at all about what would happen if the argument were false. On a necessary assumption question, you don’t care at all about what would happen if the answer choice were true. Because knowing that something is a sufficient assumption doesn’t tell you anything about whether it’s necessary, and vice versa.
There’s a bit of a fine line between flaw questions and assumption questions, and in reality, it doesn’t matter too much. What about the possibility that you can do well on the LSAT without studying (my earlier example)? If it never occurred to me, technically, I’ve probably committed a flaw. If I considered it and disregarded it, I’m making an assumption. But either way, if it’s on an LSAT question, getting the question right will rest on the same thing, whether it’s a flaw question or an assumption question – recognizing that according to the passage, it’s necessary to study to do well on the LSAT. If you catch that, you’re going to get the question right. Of course, on the actual LSAT, the relationship is going to be hidden a little more than in my example. That’s what the LR section is all about – using complex subject matter to obscure fairly simple logical relationships.
Hope this helps.