Well, unfortunately I don't know the american way of gauging wires, since everything is metric over here (Germany)... But here is my opinion anyway.
My impression was that the speaker wires were 0.75 square mm at the most, probably less. But electrically they will do for most Applications, unless you do an SPL job and want to have four kick-bases in the doors ;-)
I would suggest using the original wiring for the part that goes into the doors. I have personally made two installations into all four doors of both my Mondeos... The first time I ran new 2 x 1.5 sq.mm wires THROUGH the door connectors (2.5mm wires I couldn't get to fit). That was a major PITA to do. In my current Mondeo I use the original wiring in the rear doors (I ran new wires from the Amps up to the b-pillar and tapped into the original wiring there. For the front doors I bypassed the connectors this time and ran new wires through the rubber grommets in the A-pillars and the doors. Now I have a short piece of wire visible there when the doors are open. MUCH easier to do obviously.
Still I would suggest using the original wiring for the door connection. Run new wires up to the door pillars and tap into the original wires there. That is what most installation articles in the magazines over here suggest, unless you really want to build a High-End solution.
Just my opinion. Good Luck with the install!
Joerg