I have an 02 WRX with a Sony CD player. It's supposed to run at 40 watts a
channel and is considerably louder than the stock cd player. I just
purchased an amplifier that is 80 watts a channel an i will be using this to
power my speakers. I'm not looking to run my system louder, but cleaner.
The built in amp on the Sony was loud enough, but it runs a little hot. I'm
hoping by not using the internal amps that it will run cooler.

my question is, if i install the amp in the trunk or under a seat, should i
replace the factory speaker wire? Is it ok to run the wire to the headunit
where the current ends of the wires are, or should i completely redo the
wiring?

Any suggestions or discussion is appreciated!

It won't be necessary to upgrade the speaker wiring unless there's
something seriously wrong with it. But, from the sounds of it, it appears
that it worked well before so you should be set to go.