They'll happily work together, the signal (unless you tell it otherwise and few HU let you) comes out of every socket at once. Unless you change the balance etc and tell it otherwise (no left noises if you turn off the left side etc.).
Your speakers will work just fine with the sub hooked up.
The remote lead is purely to tell the amp to turn on when the HU does.
On your sub (found the pics) on the low input side, push the slide switch to LPF and assuming the dial on the left of it says 30-250 turn it about half way round, about 110mhz - this tells the amplifier to ignore the higher frequencies as they're not a subs job.
Then turn the Bass Boost setting the f*ck off, because it's bad for you. It's not what it says, you don't want it

The "level" dial is most likely what everyone else calls gain, rough set up of this is to turn your HU to 75% volume then turn the dial on "level" until you hear a distortion, turn it back a touch and you're done.
This is really napkin set up stuff, but it shoulf get you started.
From there you can shape the music from the HU with the EQ or whatever it has.