A subwoofer is a speaker in your car stereo system that produces low frequencies 20-80 Hz that midrange and even mid-bass speakers cannot reach. These low frequencies come from instruments such as the kick drum, bass guitar, bass drum, and my favorite the double bass.
A subwoofer reaches the lows in bass that woofers can’t reach, and will even free your other speakers to deliver better mids and high frequencies that they're designed to do. Without a subwoofer you won’t hear or feel the benefits of those instruments.
15 inch subwoofers offer the most powerful and deepest bass thanks to their big size. They mostly have bigger magnets and the cone surface area is bigger so will move more air.
There's no correct answer because everyone's taste is different. The most common sizes are 10 inch and 12 inch subwoofers, but a 15 inch sub will drive the loudest and widest bass.
2 x 10 inch subwoofers will punch harder than a single 12 inch sub, because the combined cone surface area of 2 x 10 inch subs yields more sound pressure . That said, a single 12 inch subwoofer will likely sound deeper. But when shopping for a subwoofer, it's important to note that the size and travel of the coil / magnet will have more influence on the power than the cone diameter.
It's the box that you keep them in. They're also called Subwoofer Boxes and they're usually covered in grey carpet material. There are different types of subwoofer enclosures, the most common being sealed, ported and bandpass boxes. Different subwoofer boxes all produce different bass so make sure you know which one is to your taste before choosing the right one.
As long as the car amp is designed to be stable at 1 ohm then it's perfectly fine, but if it isn't then you shouldn't push a 1 ohm sub from the amplifier.
The main difference is that active subwoofers have an inbuilt amplifier, where passive subs require a separate amp to run them.
Ported boxes and bandpass boxes will give you the earth shaking bass that many associated low frequencies with. That said, a sealed enclosure will give you loud volume, but the bass will be more accurate and not as boomy as the other enclosures.
It depends on the impedance and the RMS. Basically, your amplifier must be able to push more RMS power needed at the impedance you're driving. The amp you want will have to be capable of powering 75% to 150% of the total RMS rating for the entire subwoofer system you have.