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The cheap charge controllers with an LCD voltage display are excellent value for money, but they don't measure how much energy is being produced or consumed, and the firmware can't be modified to support different battery voltages or chemistries.
Not impossible, but it's unlikely to be cost-effective compared with buying an amp (new or used). The LM3886 can be paralleled to increase the current (and handle lower impedance loads), and then bridged to double the voltage swing (and roughly quadruple the power).
It's possible. Consider starting with a bare circuit board from ebay, or a kit, or even a completed board. Bare PCBs are dirt cheap, and will make for a much neater build.
Also, signal to noise measurements, and frequency response. RMAA could do that using a computer sound card, except there is the problem of the bridged output. I'd try a sound card with optical input and a battery-powered ADC with optical output (eBay, analog digital audio converter).I suspect performance will be unimpressive, since there's no feedback. Suitable for a vehicle PA horn or siren, the kinds of music production applications where distortion is a good thing, or a science fair project. If you actually want to listen to music, there are awesome little class-D amp boards from China for the price of a burger combo.
In my experience, solder gives way or flows under pressure so that screw or clamp terminals don't stay tight. It's better to put a ring or fork or ferrule terminal on the wire, as appropriate. If that's not practical, then just solder the very tip of the wire to prevent fraying.
there's a bunch of potential reasons for linking the radio into the vehicle bus. discouraging aftermarket stereos, theft protection, knowing when the headlights are on, different eq profiles for different models or perhaps according to speed or window or convertible top position. I'd guess this stuff started happening in the mid-'90s. radios from the '80s would be safe bets, and not so old that wrecking yards would call them collectible.
Some late model car radios aren't usable unless they're connected to the car's computer bus. I don't know when that became a thing. They do it because it simplifies connections to steering wheel controls, and because a radio can automatically use different EQ curves for different vehicle models, and stuff.