(1) LEDs can in fact be dimmed by running less current through them, however their power efficiency drops, which negates the whole purpose of LED lighting. The most efficient way to dim an LED is to strobe it on faster than the human eye can detect By varying with fraction of the on/off cycle that the LED is on, the human eye perceives this as "dimmer".
This isn't the whole story. Dimming a LED by using less current makes it more efficient, because LEDs are more efficient at lower temperatures.
It is the driver circuit that can become less efficient. If the driver circuit uses 5% of the power, then when you dim to half power the driver circuit may be using the same power, which is now 10% of the total power. Your efficiency has gone from 95% to 90%. Incandescent globes and fluorescent tubes lose even more efficiency when they are dimmed. A linear regulator as a dimmer is inefficient. You need to use a switch mode regulator. These can use filtering to avoid the flicker, but this makes them a little more expensive.
LEDs and Fluorescents are about the same efficiency (give or take 20%). LEDs are better for dimming, rapid turn on, and narrow beams. Fluorescent are better for area lighting.
LEDs lights should be built with custom fixtures for several reasons. Firstly they need to run cool to be efficient, and this needs the cooling to be built into the fixture. Secondly they are point light sources and very annoying to the eye, requiring the use of diffusers. Finally, a single LED is currently about 3W maximum, so for a room light you need multiple LEDs, which means it needs to be bigger than a conventional incandescent globe. You can fit 10W of LEDs into a ES or BC style globe, but it isn't ideal.
Heisenberg may have slept here...