Great job Max!
To sumarize then: the Flashback 3 is a controller. The EasyLase USB is a controller. They do the same thing - they receive signals from the laser show software on the computer (via a usb cable) and send analog signals to the scanner amps, and blanking signals to the lasers. That's about it in a nutshell. The FB3 *also* has the added feature that allow it to run independent of the computer and to display files that are stored on the memory card, but it's unlikely that you'll be using it like that...
If you mount the controller in a box that sits between your computer and your projector, then you need to run a 25 pin cable between the controller and the projector. (When you hear people talking about an ILDA cable, this is the cable they're talking about.)
If you mount your controller inside your projector, you won't need an ILDA cable. You'll solder the wires to a 25-pin plug inside the projector and just plug it into the output of the controller like Max explained.
Re: the green dot to the left of the first dichro in the picture you linked to... The dichro isn't perfect. Although it will transmit 95% of green light and reflect 99% of the red, you are always going to have some losses. The green dot is the 5% that didn't get transmitted and was actually reflected by the dichro. Yeah, that power is lost. Such is life. (Look very closely and you'll see antother greenish-yellow spot to the left of the second dichro where the beam reflects off that face too.)
Adam