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Those wires are only transmitting noise. There's no danger of anything bursting into flames there (unless something's SERIOUSLY wrong hahaha!) .. the larger the wire, the less resistance there'll be meaning better noise (essentially... )
Hmm good point. You're missing either sound input or power if that is the only connection on the sub !? Is there a phono connection for sound somewhere else on it..?
Active sub is basically a sub+amp in a box. Passive sub (not really the right technical term imo) is just the sub and you connect it to an amp yourself (which will be powered).
Again, an "active" sub is just being powered by the amp in the same box. The wiring is exactly the same. The amp is powered, and has a remote cable to switch it on/off with the car. The amp then just has 2 wires going to the sub (in most cases) which sends a current to move the cone.
If you buy separates you'll have a sub that literally just needs amped + and - wires connecting.