ITX > Not my lane. Using mATX.
TS > Get you a liliput. 7" 16:9 or 8" 4:3. Your choice.
Speakers > You will need an amp. Even the best soundcard doesn't have any amplification.
Power: Do NOT hook into the cigerette light outlet unless you wanna possibly blow some fuses. The cig. outlet is not made for a lot of power. Go directly to your battery using 8 gauge wire. Better yet. Ditch the inverter and get an OPUS. An inverter will not be able to kept running when you start your car. The OPUS can and has some extra features such as delayed shutdown and remote start (via ignition).
Sound: 3.5mm to stereo RCA cable. Take this and plug it in from the soundcard to the HU/amp.