****, what kind of installer takes those kind of shortcuts!? Yes, your power wire should run directly from the positive on your battery to the amp or distribution block(for more than 2 amp)with a inline fuse less than 18 inches from the battery.
The remote turnon wire should be wired from the back of your HU. There is a wire specifically for that, I think its blue.
Make sure your grounds are good too, seeing as how the rest of the install is bad. make sure they are as short as possible and attatched to bare metal with any paint stripped away.
EDIT; With that much power, I'd say go with atleast 4gauge wire, I'd recommend atleast 2gauge though.