We're building a new multi-panel video display wall at my office, and I put quite a bit of research into LCD panel technology -- with an eye to long term constant usage.
1. Burn-in is a bit of an issue, but not a horribly serious one. LCD panels will "burn-in" but the effect is temporary. Basically, any time you put up any constant, non-changing image on an LCD screen, it starts developing a "memory" of that image. This memory will cause the image to remain up on the display even after the image is supposed to be gone (burn-in). However, unlike CRT burn-in, this memory doesn't last forever, but fades over time. The length of time this takes is directly related to how long the image was originally actively displayed on the screen. So, if your system is going to be displaying one static image all the time, you might end up with some "burn-in" but it won't be permanent (but you still might want to look into turning on a screen saver type feature). I should note though that even with very extended static image displays, the "fade time" is really quick. I'm just noting that it is different when you might leave the same image on the screen for 1-2 years constantly (or nearly constantly).
2. Backlights and length the displays last. LCDs are lit from behind with a florescent tube lamp. Like any florescent tube bulb, the first time you turn it on, it starts slowly becoming dimmer and dimmer over time until it eventually burns out.
The backlights used in LCD displays currently are generally rated for roughly 6 years of use before they reach 1/2 their original brightness. Some lamps are specifically "built" for more constant use, and some are "built" for more on-off sporadic use. However, this is mostly marketing, and both types of back-lights generally "last" almost the same lengths of time (the constant rated ones have different "aging-brightness curves" than the others). So, that 6 year mark is when the display will still work, but it will have become so dim that it may not work well anymore, but it will have happened slowly over time. Of course, there are still occasionally "catastrophic burn outs" but these are generally rare. So, shutting down the panel would certainly help save some power (and would help cut your carbon footprint), but it won't make much more than a few month difference in the active-use life of your display (of course, if it's on when you're not using it, then it's using up those hours and if you have it off when not in use, then that 6 years could stretch out for much longer).
While it is certainly technically possible to replace the backlight in a LCD display, it is not typically financially beneficial to do so, because of the swift change in the LCD display market (and the high cost of the repair).
LCD technology is moving now to replace the tube bulbs in the displays with LED backlights. This is beneficial for a number of reasons. One problem with florescent backlights is that it is difficult to evenly diffuse the light behind the screen, so that the pixel in the top left corner of the screen is the same brightness as the pixel in the dead center. This also evolves over time (which is why even though the bulb isn't burnt out after 6 years, you might not want to use it anymore, because it will be brighter in the center than around the edges). LED lighting is much more efficient, long lasting, and even (you just have a big panel of those little LED lights behind the whole screen). LED panels can be rated for much longer periods of time (10-20 years probably won't be uncommon), will use far less power, and because the light can go all the way to the edge of the panel evenly, the LCD panels will be able to be "bezel-less" (no edging on the panel at all).
LED LCD panels are just over the horizon (Apple is shipping their laptops with them very soon). Expect that this time next year, almost all "new" LCD panels will be LED backlit.
5. Yeah, Girder can do that.
