Zoidman,
To answer your question about how a 3.7V battery can deliver 6 volts:
The common class of switching (not linear) regulators come in three configurations: Buck (where the output voltage is always less than the input voltage). Boost (where the output voltage is greater than the input voltage) and buck/boost (which can switch between either modes).
Swtiching regulators are fundimentally different from linear regulators in that they use an inductor and capacitor to store energy from the input soruce and then pass it (during the switching) to the output source. That way they can increase or decrease the output voltage any way they like, since the energy is stored before its passed through to the output, and can be "reconfigured".
So what's really important in a switching regulator is the overal power (either being supplied by the source or used by the output), since of course the circuit can't create any power of its own, rather than just the voltage or current alone.
For instance, if you have an output voltage of 4 volts and an output current of 1 amp (assuming the switcher is 100% efficient, which of course its not), for an input source of 2 volts (and a boost regulator), you would need an input current of 2 amps. because the amount of power you draw always stays constant.
Same works for buck. If your output power is 2 volts @ 2 amps, then you only need a current of 1 amp for an input voltage of 4 volts.
Switching regulators are very efficient (typically >90%) so there is almost no power lost to heat. This makes them much more desirable for applications where a fair bit of power is used (like E-cigs), because linear regulators would just dissipate the excess power as heat, and would get very hot.
Hope this helps.