Let's take one question at a time:
You're correct. Bandwidth is about how many visits you get; Disk space is about how much data you store.
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This means that you can set an upper limit of how much bandwidth your visitors use. That's useful because if you have a very popular site, then your visitors will exceed the amount of bandwidth that is included in your plan, and any excess use of bandwidth will cost you extra money. If you don't want to spend money on this, you can limit ("throttle") the bandwidth use.
You can keep your directories tidy, make sure you don't have any files twice. You can download your e-mails (use POP3 mail) so they don't take up space on the server (as they do if you use IMAP mail).
Your mail is included in the "Disk space" measurement, but only if you keep it on the server (use IMAP mail). It's not counted if you download it (use POP3 mail). Mails usually don't take up a lot of space, but if people are e-mailing you the files for your site, then your mails can be bigger than normal.
If you're trying to upload something that would exceed the limit, I'm not sure what happens. I think that you can upload a file, but after that you can't upload any more until you clean out enough to fall below your disk space limit again. It could also be that there is a lower disk space limit assigned to the FTP user than for your web space in general - check the user account https://panel.dreamhost.com/index.cgi?tree=users.users& and see the second number under "Disk Used" - that's the limit for the user, and it may be lower than the total limit for your disk usage (https://panel.dreamhost.com/index.cgi?tree=status.disk&).
Hope this helps -- otherwise please post again.
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