I've never hooked up an integrator on a Suzie, but I've done a couple Yamis and it probably isn't too different. Odds are if it works the way it's done, it's done right -- if thats the case, just shorten the wires by cutting and resplicing.
For a clean new install I'll typically reroute all the wiring under the trunk above the undertail. The taillight assembly connector should hook into the stock wiring, and the single wire for each flasher is all you should need to splice. The cut off wires you referred to are most likely the old ground wires from the flashers. Since your tailling is integrated the flashers will most likely use the common ground for your taillight... remember all of this is based on assumption that you have the correct light for your bike and the dude before you didn't completely botch the job.
Also the flash rate difference can be fixed with a resistor. I couldn't tell you which resistor to use, but just go to your bike shop and buy a few different ones of varying resistance. Slap them in, one at a time, on the circuit for the light that flashed faster. Once you figure out which one to keep, take the rest back for refund.