Do I need another amp for a sub-woofer?

[Alien Mantis]

Nice photos!

Good job. I mounted my sub amp exactly like you mounted yours.
I used a small piece of 2x2 to level my amp. The floor under the seat is uneven.
Looks like we ran our wires the same way.
I have had no problems with my setup. The amp has plenty of space around it to breath.

You don't need any polyfil in that subwoofer box. The box is already at the max size for that subwoofer. Those boxes are nice. No need to do anything to them. They are ready to go. You typically use polyfil in a sealed enclosure that is smaller, to trick the woofer into thinking it is in a larger box.
Correct size ported boxes, and larger sealed boxes do not need polyfil.

I'm sure you already know this, but if you fold down one side of your 60/40 rear seat, your bass will sound much better.
I have a hatchback Yaris, so this is not an issue for me.

Here is a couple of pics of my setup: