First, It's always nice to have someone new on the board.  A little time and reading of the postings here on the board or using the search function would have gotten you many of the answers you seek.

First:
The twelve magnet/nine coil combination is three phase.  One coil per magnet will give you a single phase alternator which will cog badly and require a very high starting torque as compared to the 3-phase.  More coils matched with additional magnets will give you more output power to a certain extent.  It also gives more resistance in the coil circuit which results in more power being lost internally as heat in the alternator.  

Second:
Three phase is recitified with either two full wave bridges (use one as a full wave and one as a half wave) or with a three phase rectifier.  Diagrams for both have been posted on here many times.  Search for 3-phase rectifier.

Third:
Make sure that you have enough water power available.  I see no reason you couldn't have a 24/18 arrangement.  I believe that if you put the magnets a greater distance away from the center, the velocity will increase but the torque available will decrease.  You might end up slowing or even stopping the waterwheel.  There will be a certain amount of power available given the size of the wheel and the flow of the water.  I have seen formulae on here to calculate available power.  Hopefully you will be able to find them or someone will reply with some help in this area.  There are many knowledgeable people on here and many are well versed in the subject of water generating.

1. The rule of thumb for a (3) phase machine is (3) coils for every (4) magnetic poles. Whether you have (12) magnets single rotor, or (24) magnets dual rotor the number of magnetic poles is still (12). This is because the rotors face each other with every magnet attracting to the one facing it. This gets tricky with the amount of force involved, and jack screws and such must be used. Potential for danger is greater with two rotors. However, if you can figure out how to get them to sandwich your stator evenly - you should see 4X the power for 2X the material. This is because when you double the magnetic field force in the gap (and through the stator), both the voltage and the current generally double in the coils. The magnets are aligned centres at 30° around some circular path, and the coils are aligned centres at 40° around an equal radius circular path as the magnets. The magnet centre to centre spacing, around the rotors should be equal to the coil leg width on your stator. The coil leg width is the distance between the middle of a leg on the left side of a coil to the middle of the leg on the right side of a coil. Your coils will be generally roundish and are dependant on the diameter of the rotor, wire guage, and the voltage you are after (more windings = higher voltage). The coils are grouped 123-123-123 as you go around your rotor, and coils 1-1-1, 2-2-2, 3-3-3 are wired up in series. All 9 coils must be wound in the same direction, and the three starts must be tagged together as neutral. The resultant output wires are 3 phase AC current flow, each phase 120 electrical degrees from the one beside it. The start of each phase (first of each of the three coils) are wired together, and called "Neutral". This is the fourth lead you were wondering about. You have 3 phases, and a common neutral. If everything is lined up, you'll be pushing and pulling electrons!
2. It is these (4) conductors that get wired to your bridge rectifier. ~AC, and diagonal from that is (AC) neutral usually not marked. You will also see + this is +DC out. Diagonally opposite is -DC out. Three bridge rectifiers handle the three incoming AC phases, and the DC outputs are wired together in parallel. From there, you can go to a voltmeter if you like, or put an ammeter in line on the +DC total out to read current flow. Or both, that is always fun.      
3. Shorter path equals quicker rotation...If torque is not an issue since you have plenty of force with the water, you can keep the generator size down with generator closer to the wheel centre, but still careful to meet the voltage you need. The water wheel can be whatever it is, but a smaller diameter rotor will give an increased RPM at certain water flow rate and therefore, increased Voltage. That is to say, unless you want to start charging your neighbours for it, and build 24" rotors with massive coils and magnets, and to heck with RPM's. Cost prohibitive to most of course. That is why selling it helps!. I guess at some point (coils and mags too far out from centre), even the water will just go around and through your machine instead of turning it.