1) It totally depends on the setup. 3 5mm LEDs driven at spec will be dimmer than 6 5mm LEDs driven at 1/2 current, but the 6mm version is more efficient. Likewise, a 5mm LED and a luxeon LED set up to provide equal amounts of light have vastly different efficiencies. However, all things being equal (equal number of LEDs, type of LEDs, etc) brighter typically means less efficient.
2) Depends. In white, I think they're pretty comparable. A luxeon at 50mA is much more efficient than a 5mm at 50mA. At spec current, a 5mm is in the 30-40 lumens/watt, whereas a 1W white is in the 25-35 lumens/watt.
Colors is another matter entirely.
3) Yep.
4) Yep. All circuits will dissipate some of the battery energy as heat. However, direct drive isn't as "efficient" as everyone makes it out to be. For one, it typically severely overdrives the LED, causing much of the additional energy being simply dumped as heat, and lowers the LED's lifespan. Two, it draws tremendous amounts of energy from the batteries, which are less efficient when delivering high power (alkalines are the worst, followed by lithiums, then rechargables)
Resistors as a form of regulation drop voltage depending on current. Current drops as battery voltage drops. As current drops, the power dissipated in the resistor decreases, and efficiency increases.
Linear regulators drop the voltage exactly the same way that resistors do, however, they adjust the voltage drop to maintian a constant voltage output, or constant current output. As battery voltage drops, current remains constant, but power dissipated in the regulator decreases, so efficiency increases.
Switching regulators convert high voltage/low current into lower voltage/higher current (or vice-versa) by switching the load through an inductor and using capacitors to smooth the output. These typically give you 80% efficiencies, but efficiency depends on the difference in input voltage vs. output voltage. Typically, the closer the input voltage is to output voltage, the higher the effeciency will be. Step-down (buck) switchers are typically more efficienct. With a buck converter, when the input voltage is a lot higher than the output voltage, the input current is substantially lower. This is a big bonus for primary cells (alkaline, lithium) as at lower currents, they can more effectively deliver all of the energy stored in the cell, leading to longer runtimes.
