Yes, they are slightly magnetized.

You can use a Bluetooth receiver to do what you’ve described. Here’s one that should work: https://smile.amazon.com/dp/B00YPATOEE You’ll also need a splitter to go from the Bluetooth receiver to your car stereo and your amplifier. However, a much better solution would be to use a high-to-low-level adapter that connects your car stereo to your amplifier. You can attach the hi-to-lo adapter to either the front or rear speakers, or to the speaker wires coming from behind the car radio. An adapter like that will be a cleaner solution and also allow you listen to your sub with the radio or anything else playing from your car’s stereo. Here’s an adapter that should work with your amplifier: https://smile.amazon.com/dp/B001EAWS3W And you can still use the Bluetooth adapter listed above to connect your phone to your car stereo wirelessly.

The 3 larger pins on the outside are mainly to hold the USB port in place. There’s no electrical signal connection in them, and they just provide a ground shield to the outer USB port. As long as the 4 smaller pins are making good connection with the circuit board then you should be fine for power and signal. Just solder the 3 larger pins in place to keep the USB port tight and stable. If the USB port is loose due to loose connections on those 3 larger pins, then the port could wiggle the smaller pins loose and break a signal connection. If necessary, gently bend the larger outer pins to help hold the USB port in place without it moving around. Be careful to not have solder spread across different connection or you could short something out. And you can use a small dab of glue on the front side of the board (where the USB port is, not where the solder connections are) to help keep the USB port in place.

Looks like the links that dani olivares provided aren’t working any more. Here’s another very similar product on Amazon: https://smile.amazon.com/dp/B0002J226O Or, if you need a built-in subwoofer crossover and level controller: https://smile.amazon.com/dp/B07D6JTD4V For a few bucks more, you can get an equalizer with multi-amplifer level controls and outputs: https://smile.amazon.com/dp/B00JZQYX2G

You won’t be able to hook everything up they way you’ve described. The RCA outputs of your head unit are too low to power the speakers - they are for connecting to an amplifier only. You will need to connect your speakers to either the speaker-level outputs of your head unit or to a separate amplifier. You can tap into the speaker outputs of your head unit as long as you can find which wires go to which speakers. If necessary, you can trace the wires from the head unit to the speakers to see which wire is what. It’s okay if you can’t tell which is + and - because you can wire them up either way and it should work. If the speaker polarity is reversed the worst that can happen is poor sound quality and then you can reverse the wires to check if it improves. Since you have the RCA outputs on the head unit, you could easily add an amplifier if you’d like. Basic amps aren’t too expensive and you don’t need anything fancy. They do add a level of complexity to the whole installation so maybe consider professional...

There are lots of electronics shops across the country that do repairs on car stereo amplifiers. Unfortunately repair costs often start at about $100 and go up from there. So sometimes it’s not cost-effective to have the amp fixed when you can buy a new replacement for around the same price as a repair. Look for a repair shop that will give you a free estimate before the repair is done. If you do have it fixed, try to use a shop that’s certified by Sony. But some repair shops do excellent work even if they aren’t factory certified for your brand of equipment. Check online reviews and word-of-mouth from previous customers.

The amplifier might not like the subwoofer’s 1/2-ohm load. The amp can do okay at lower volumes, but when you turn it up the subwoofer is too low an impedance for the amp to handle and it goes into protection mode. Check to see if the amp is going into protection mode - it should have an indicator light somewhere to tell you. Even without a protection light, the amp might be shutting down it’s output because the impedance is too low. You can switch from parallel to series wiring on your sub’s voice coils. That will bring the load up to 2 ohms which might work better for your amplifier. Keep in mind that amplifiers capable of running sustained 1/2-ohm loads at high volume are pretty rare (and expensive). Your amp is probably going to be a lot happier (and more stable) with a 2-ohm load or higher.

Try testing the camer’s power connections. Maybe when you tested the camera using the separate monitor, the camera was getting a different power connection or source. Put the car in reverse, make sure the H/U is showing the backup screen, then check the camera’s power (at the camera) to make sure it’s getting 12V. You can also try connecting the camera to constant power instead of switched power temporarily. Some Pioneer head units run a video signal input check when they’re first turned on. If no camera signal is present, it might cause problems. Also see if there is a camera power connection on the Pioneer H/U. It might be necessary to power the camera from the H/U instead of elsewhere (such as tapping into reverse lights).

Set TWO might be a mono subwoofer output which would only need 2 pins. If set TWO is a stereo output, it might use the same signal ground as set ONE. So the 2 pins in set TWO are the positive connections, and set ONE and set TWO share a common (negative) signal ground. This is just a guess, so you’ll need to check and make sure. Assuming these are all truly low-level preamp outputs, you should be able to test these out relatively easily with little risk of damage. Try running the pins from the preamp output of the radio to the positive (center pin) input of your amp. Then connect the negative (outer ring) input of the amp to ground. This might not have good sound quality, but it will at least help you troubleshoot which radio pin goes to what channel. Just be sure to not connect any of the radio pins to ground. If there’s a preamp pin that’s labeled negative or “ground” on the radio, then it’s probably a common negative connection for all the preamp outputs. That one pin can be used for all your preamp...

Pandora and Bluetooth can sometimes be finicky when used together. Pandora updates their service often, and that occasionally wreaks havoc on the Bluetooth connection, especially for car stereos. Here are a few things to try: (1) Make sure you’ve got the latest version of Pandora software - check for app updates. (2) Make sure you’ve got the latest version of OS on the device you’re running Pandora on. (3) See if there’s a firmware update for your JVC car stereo - there probably isn’t but you can check on JVC’s website. (4) Use the USB input on your JVC car stereo instead of Bluetooth - the USB connection is likely to be much more stable and trouble-free. Most JVC car stereos will let you keep the Bluetooth connection live for making calls even when you’re using the USB connection for streaming music.