hope this helps in answering few of your questions.
1. the main purpose of the Franken-Naks is two fold: 1) drastically reduce the size for stealth applications and 2) run the naks on phantom power.
2. Franken-Naks must be powered by phantom power (P9-P48) via an impedence transformer (eg. AT, Samson). phantom power comes in various voltages (P48 being the most universal and popular).
3. the system is "active" becase it separates the capsule assembly (cmX00 + cap) and the "body" (module.. eg. AT8533, etc.)
if you look at the schematic above for the pre-mod, you'll notice that BOTH the signal and the supply voltage is riding on the same conductor. (this is analogous to SP's powered mics via a mini plug. (2 conductors per mic)
now look at the schematic for the post-mod, you'll notice that the signal and the supply voltage are separated, hence....3 conductors. (this is analogus to AT853rx)
with that said, you can NOT run the Franken-Naks with a simple battery power. however, powering schemes like the new jklab's PP9 will work since it also runs on the 3 conductor scheme.
hope this helps;
marc