OK, first thing I would do is have the alternator and battery tested. I would have the battery tested simply because it is part of the affected system and since it is new, it could be bad. If you have a multi tester, you could actually test the voltage on the battery to see if it is high. I think anything over about 13.5v is too high for a resting battery. Then use the multi meter on the alternator to see what kind of voltage it is putting into the battery. My logic meter would say that the battery is getting much higher voltage from the alternator than it should. I think something like 14 would be normal. In the video you said you can hear the battery "fizzle". That is your battery being "cooked or boiled" from being over charged. The radio making noises is also likely from being fed more voltage than it can handle.
Don't run the truck any more until you figure it out. You stand to fry not only the battery but a host of electronics in the truck, least of which is the radio.
I don't know exactly how the charging system works on newer vehicles, but they used to have a device called a voltage regulator. That device did what its name implies and regulated voltage off the alternator to the vehicle and battery. I had a car and for a long time I could smell "sulfer" after I drove for a while. FInally, one time, I opened the hood and could see and hear the acid in the battery "boiling". It was the voltage regulator gone bad. Replaced that and all was well. I am just lucky it didn't blow up the battery, which is a common result of overcharging and boiling a battery.
Now a days, I don't know if they have such a device or if it other wise regulated through electronics or part of the alternator itself, but I am guessing your truck is being fed way to much voltage.
Check the systems with a multi meter if you have one and know how to use it or better yet, have it checked by a shop or auto parts store (free usually). Just run it as little as possible. Towing it might be a better option unless you can get the alternator diagnosed at your home and if bad, replace it there....very easy process.
