Cut the wire end in picture one...Use a butt connector and crimper with a Male spade tip so that the wire in picture 1 looks exactly like the wire in picture 2. Then plug the wire from pic 1 into the harness in picture 3...

 

I actually got everything working properly now.

Radio still gets kind of hot in the back during use, but everyone said that the aluminum block acts as a heat sink for the built in amp

 

Good to hear its working..fyi 160 watt speakers are designed to run at usually betwwen 55 and 75 watts rms (continuous wattage to power them correctly) with 160 watts being peak.... most car stereos are designed to put out 45-65 watts peak per channel and 15-25 watts rms..(and thats with audible distortion at that output).. Do you see the problem here when tring to push beefed up large magnets and heavier/stiffer cones with 25 watts when its designed for twice that power to drive them? the speakers usually distort at much lower volumes because the stereo cant power them properly and people turn up the bass and such to try to get that full sound which only makes matter worse.
The system is not matched properly and this is why a 7watts factory stereo system that is matched up properly with the speakers can sound better than many aftermarket setups people put in without understanding this.
If you have component speakers with separate tweeters and crossovers be careful to check the ohms load they are putting out... they can run at 2 ohms instead of the normal 4 and this will put more of a load on factory stereo amps causing them to run hotter...

 

My stereo is a 52/w
The 4 speakers are are 50w/nom 160w/max