On the south side of the border, I usually tell folks to visit an autoparts store as they will check the alternator output and battery voltage for free.

I suspect the alternator brushes are getting bad and need replacement. Unfortunately, I think you need to get a new voltage regulator as I have yet to see any brushes sold separately. The alternator should be putting out 14.5V, or close to that.

The red wire at the battery getting hot is not a good thing. If your volt meter has needle probes, stick the red wire about an inch down through the insulation and take another reading. The end of the wire at the battery is exposed to the elements and can get pretty bad. Replacement of the large wire is quite expensive. Then again, warm is normal but almost burning hot is not.

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My back feels better when I sit in a Volvo seat