1. Frame sizes are the same between fixed gears and road bikes. Whatever frame size you rode on your old bike will apply here.
2. Fixed gear means if the wheel is turning, so are the pedals. You pedal backwards, the wheel goes backwards. Single speed involves a freewheel so you can coast, meaning you can stop pedaling while going down a hill.
3. You can convert and old road bike for a lot less than $350, but if you want an actual "track" frame, the Kilo TT from bikesdirect.com seems to be popular as an entry level bike for $350.
4. Fixed gear gallery has a lot of pictures for you get ideas, or you can just check out the sticky picture thread at the top of this forum.
The rest of you: Be nice. At least he is trying to understand what a fixed gear bike is before he buys one.