I couldn't get enough Zoltan crew members to test it myself, so I wonder if getting 4 of them in the weapon control room will increase total weapon power capacity from 8 to 12 or if the 4 power bars will be freed instead. I'm thinking of finding 3 5-shot laser cannons for a grand total of 15 destructive shots.
No, Zoltan crew members will only fill the available bars for the room they occupy, freeing up reactor power to be used elsewhere. This can easily be demonstrated by the Zoltan Cruiser Type A, by moving the all three starting Zoltan crew members into the engine room, which by default only has 1 bar:
The energy provided by the Zoltan in the engine room will not exceed the limit of the system they are in. If you've upgraded weapons to maximum (8 bars) and cram the room full of Zoltan, all that would happen is that 4/8 bars are being powered by the crew, freeing up your reactor to power other systems.
It should be noted that the piloting, sensors, and door control systems do not actually draw power from the reactor, and any Zoltan crew placed in those positions will not contribute to your ship's power levels.
There is a benefit to stuffing more than a single Zoltan into a room, beyond the reduced load on the reactor. As pointed out by @BlackVegetable in the comments - the energy provided by Zoltan crew is impervious to ion damage; so two Zoltan in the shield room will mean your shields cannot be taken completely offline by ion weapons.
No. You cannot go over the maximum total power capacity of a station by overstuffing it with zoltans.