1) "High Intensity LEDs" can mean anything from 30mA//20mW to 1A/12W.....so you need to define how much light you require first.....Ebay-China is a good source for cheap LEDs....
2) See # 3
3) ****NOTE**** I did these calculations based on 4 R44 Batteries....Adjust for 3 as you see fit******
The R44 batteries have the following output range:
Alkaline: 1.5V//150mAh
Mercuric Oxide: 1.55V//200mAh
Zinc-Air: 1.35V//600mAh
(From Wikepedia:
http://en.wikipedia.org/wiki/LR44_battery)
Assuming the Zinc-air Type @ 1.4V//600mAh....in series --> 4 * 1.4V = 5.6V//600mAh
Assuming an LED with a nominal Vf of 3.2V to 3.6V (typical of "white" LEDs) and a nominal current of 30mA...
If you connected the batteries in Series and the LED's in parallel you would need:
(5.6V - 3.4V) = 4 * (0.030) * R ==> R = 18.3 ohms ~ 18 ohms (closest standard value)
Assuming the 18 ohm resistor, the power lost in the resistor would be 18 * 0.12^2 = 0.2592W ==> 259.2mW
And the power delivered to the LEDs would be 3.4V * 4 * (0.030) = 0.408W = 408mW
With the total power consumption being ~672mW..
suggesting a total system efficiency of ~61%
the battery life @ 120mA would be roughly 5 hours.
If you replaced the resistor with an 85% efficient Constant Current Converter your consumption would still be 3.4V * 0.120A = 408mW,
your system power consumption would only be 408/.85 = 480mW
And your batter life would be (5.6V * 0.6Ah)/0.480 = ~7 hours
4 * 100mW LEDs is almost exactly the light-output equivalent of a cheap pocket sized LED flash light and with your battery selection the battery life is ~1/4 that of a similarly sized flash light using three "AAA" batteries.
So...if it were me, I would likely just buy a $2 flash light ;-) But if your project requires the R44 batteries then there you go....
Fish