Yes, you want a CC driver or three, depending on whether you have enough voltage to run them in series. Current must match the desired current in the emitter. Voltage must be greater than the max voltage the emitter might require to get that current. Matching power specs can get you in the ballpark, but it's only a guide, not the final answer. Links don't work so I can't check out what you found.
As far as running them in parallel, it depends on the application. Right now I'm supposed to be working on a light that uses 30 LEDs, in 10 strings of 3, one group is 4 strings in parallel, the other group is 6 strings in parallel. My customer has put hundreds of these in the field over the last few years, and they are working so well, the mod I'm making is to push the currents higher. But they are 30 leds from the same batch, mounted on the same large heatsink, which is capable of dissipating the max power with only natural convection. Here's the potential problem - if one emitter gets hotter than the others, it's voltage drops. Since they are in parallel, it's voltage can't be different, so instead it draws more current. It heats up even more as the others cool off. If it's bad enough, you get thermal runaway, and the cycle continues until the hot emitter fails. If it fails open circuit, the current is all dumped into the other two, which also fail in rapid succession. This is much more likely in your application, where you will likely get three from the same lot, but not necessarily, and you have three different heatsinks, which require active cooling, with the nearly inescapable possibility of one getting poor cooling while the others don't.
Running water cooling in cast alu heatsinks should work quite well, as long as there's water flow. Close is good, but you don't want to get so close that you have temperature bands across the emitter where the cooling tubes are! I don't have a good answer for how close is too close, but if I were doing it, I would shoot for the distance from the tubes to the emitter being about half the distance between tubes, and not less than half the diameter of the tubes.