Different LEDs in parallel

The most efficient method to do this would be with a boost converter, preferably one that has current control. Hundreds of LED drivers which are essentially modified power ICs are available nowadays, including ones that operate from single alkaline cells down to 0.9 V e.g. the Micrel MIC2282 (for more look up "single cell led driver") which should be able to drive up to 33 V strings (~8 LEDs), though asking it do that from a single cell may be pushing it

In a previous question, I did actually recommend a power IC, the Linear LT1618 (not outwardly marketed as an LED driver, but an application schematic showed it as one)

Whatever you choose, powering (20) 20 mA LEDs from a single alkaline cell is probably not feasible just because the voltage will dip so low with that load it will undervolt most controllers. If you could use two, you'd probably be in business.

If these are 12V LEDs then they most likely have some sort of regulation built in, so you don't have to worry about putting in a resistor. If you have the documentation for them, I would put it in your post.

2) If you wanted to put resistors within each parallel circuit, it would also need to have the same resistance as the one you would put at the beginning or end node, not 1/5. The advantage of doing this is that you could have smaller resistors rated for a lower power than one big resistor rated for a high power.

3) Short answer, no, the resistor is generating heat that would have been made at the LED if the resistor wasn't there.

4) Those don't sound like regular LEDs, but if you mean LEDs like the through hole 3mm or 5mm most of them are indeed designed for 20mA current draw at a characteristic forward voltage.

LEDs are non-linear semiconductor devices, their current draw is non-linear with the voltage across it. Look at this graph to see what I mean. http://en.wikipedia.org/wiki/File:Diode-IV-Curve.svg