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Well, I'm a noob on carputers (been lurking for months here and self-teaching Photoshop, Flash, etc), but I've done car audio for many, many years.
Q1: This is one leg of what is/was known as the "big 3". The other being batt+ to alternator, and batt- to engine block. If you do the batt+ to alternator wire, don't overlook fusing (using a fuse or fusible link).
Q2: Becomes an issue only if you find yourself with ground loop problems. However, a rule of thumb is that anything in the audio stream should be connected to a common ground point to help avoid ground loops (and attendant alternator whine).
Q3: 12 gauge is fine for your proposed sub, 12 is overkill for the main speakers, but won't hurt anything (16 would be OK).
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