Well, to get past the very high voltage you can just make a Cascade Multiplyer from a 9V battery or two to power 20 or so LEDs if need-be.
Im not certain if you'd need 1.5V for each LEDs, the amount of power drawn from 3 1.5V LEDs should run on a pair of AAAs without much issue-though if you used a pair of AAAs with 1.5V LEDs to lower the voltage to about 1.5-1.7 a 100 Ohm resistor would do the trick.
A switched capacitor circuit is typically more complex than just using a higher voltage battery or splitting the LEDs into several parallel branches. Though yes, you could do that.
You're mixing voltage with power, two distinct things.
That all depends if you're running them in series or parallel, if you're talking in parallel yes, for two AAAs, you want a resistor that will provide a voltage drop of 1.5V and will act as your current limiter.
If you have three LEDs in series, two AAAs may power them, but they will be dimmer as they're not getting a proper 1.5V each.
The standard forward voltage drop is 1.5V for a diode, standard LEDs are actually closer to 1.7V each but for simplicity's sake, 1.5V works.
That said, it varies by colour and brightness. Red LEDs consume the least, so always check the specs on the LEDs you've purchased.