1) It depends on what applications I'm looking for mainly but build quality and parts used also come into account when picking out any speaker. A higher xmax isn't always a good thing, depending on what you're looking for out of the driver. I think parts used and reliable parameters are one of my biggest concerns.
2) Well, they work by taking an input signal and boosting that signal and outputting it. But I'm sure you already know that. If you want to understand their design, you would need a college level modern physics education as well as a semiconductor fabrication/physics understanding. The transistors are the backbone of the amplifier and they are basically a slab of semiconductor material that has been doped to either have a positive charge (P) or negative charge (N). When you put them in a row of either NPN or PNP types, you have a transistor. If you apply a voltage to the joined pieces, you induce a current. By applying the correct voltage to the correct spots, you can achieve gain. You do need a DC power source as well as a small signal voltage (usually AC and in audio amplifiers, this is the voltage that comes from your headunit through the RCA cables) in order to have the results you're looking for.
As far as the heat sinks go, the transistors will be passing a large amount of current and current leads to heat. This heat has to go somewhere or else the semiconductor material can start to break down and the transistor (or whatever component) will begin to operate outside of a linear region causing either breakdown or destruction. The heat sinks are usually always attached to the power house transistors and they help take heat away from them. Heat is just another form of energy and travels from high potential to lower potential. Some objects work better to transfer heat and others do not; just like some objects have a higher or lower resistance than others. The heat sinks take heat away from the transistors and release it to the air. The reason that you see many heat sinks with many "fins" and whatnot is to increase the amount of surface area exposed to the air. The more surface area, the better you will get rid of heat. Just like the more clothes you take off, the colder you get because you're releasing heat into the air.
There is way more to it but hopefully it's close to what you were looking for.
3) Not too long ago, a thread was started about this and Nick from Incriminator audio had some very helpful posts answering this very question. It would be worth searching for.
4) People love to vote for their team. People also love to be part of a small group and don't like to be associated with the masses. Since JL has become such a big name it is today, it is widely taken in by the masses and marketing (read prices) tells them that this is the best you can get. Since the masses love to show how they're not inferior to anybody, they flaunt this idea that JL imposed on them. The other people that like to buy the esoteric equipment think that they have the best you can get for your money and so they like to flaunt what they have and how lesser known it is. Two people thinking they're superior to one another can only lead to arguing and fighting. And what better place to fight than on the internet! Here, you can remain anonymous, argue all day long, insult people without repercussion, and leave an argument anytime you choose.
So, why wouldn't a thread with JL equipment mentioned not get tons of views and tons of "overpriced" arguments thrown around? I mean, it's like walking into Iraq and trying to ask them how they feel about Christianity -- it's not going to end well in either situation.
Hopefully this was helpful and not too long and ridiculous.