Your dad is on the right track, that it is smoking because you are pulling too much from your cig port. Hence the classic picture:
1.) No. Regular cords are meant for AC. Meaning they dont actually draw as much as a DC cable needs for the same thickness. If a cable of x diameter is needed for AC of some voltage, a cable of 2x or 3x diameter is needed for DC. (not actual numbers, but you get the point). You could take multiple cords (not for length) and multiple wires would carry the same current. So if you had 6 extension cables with 2 wires each in them, wire side #1 of all 6 to the battery, and then side #2 of all 6 cables to a ground point. Now this becomes pretty messy and unless you have lots of cables lying around, you are better off just buying a good cable to begin with. And it will look nicer! If you go to walmart, you can get a 4awg or 8awg amp wiring kit for like $20-$50 that has all the wires you ever need. If you go to Circuit City or your local car audio shop they will sell good quality (and low quality too) power cable by the foot. Expect about $1 to $3 a foot for cheap to mid-range power cable.
2) Within 18" of the battery on the + line.
3) There are a few inverter SDC circuits on here. SDC is short fr SDC. You may want to look into this voodoo magic box we call a DC-DC PSU. No need for an inverter as an inverter is messy, inefficient, and cause tons of problems.
What are your system specs?