@callofcthulhu nailed it with his responses. A couple things I would add:
Does the GarageBand manual really state that, or are you going by what you've heard online? I don't mean that in a snarky way. The whole "record as hot as possible without clipping" thing has been around forever, and it makes no sense in the modern world of digital recording. Shoot for -18 to -20dbfs on the peaks (some folks go up to -12 to -14dbfs, which is probably fine as well provided you don't have a super dynamic input signal).
A quick Google search provided me with over a full page of articles explaining how to increase waveform gain, so yes, GB does let you do it. Just like anything else software related, you have to take the time to learn how to do everything you want. Google is your friend in this regard. There's an insane amount of information out there for people in your position. Take advantage of it.
Yes, but that's not the point you were making. You were talking about input signal levels which is a function of things happening in the analog domain, not the digital one. Just because the signal is passing the converter doesn't mean that adjustment made in the box will have an affect on things happening outside the box.
You can, which is what I stated above and in my previous post. Those adjustments have nothing to do with the input signal and are used to resolve different issues, not the ones you're having. Moreover, once a signal is clipped, it's clipped. Lowering the volume/gain in the box will just make the clipped signal quieter. When you exceed 0dbfs, all of the 1s and 0s become 1s and you get harsh, nasty, unpleasant digital distortion. There's no reason to track that hot in the digital domain. You can pleasantly clip a preamp in the analog domain and then use something to attenuate it prior to crossing the converter, but that's a very different thing.
That works fine provided you're not clipping. That said, if you're hitting -18 to -20dbfs, why bother? You're already at the optimal level for mixing.
Why can't you do that with the Jam? There's an gain control on the side of the unit. Reduce the level and track the part again. You shouldn't be tracking so hot that you're exceeding 0dbfs (i.e. clipping) anyway, but I understand that accidents do happen.
Don't get caught up in what the waveforms look like. The notion of halfway being "about right" is silly. The noise floor in the digital world is so low that it's a complete non-issue. Trust me; Record at -18 to -20dbfs and you'll have a much better time.
Volume, yes. Tone, no. It's digital. Changing volume only changes volume, it does not have ANY affect on tone outside of things like Fletcher-Munsen curves.