2004 Volkswagen GTI VR6 Battery problems?

I bought this car on Saturday with 105, 000 miles and it has an aftermarket Pioneer head unit that you can play music through iphone or ipod. The first day I got it, I sat in it without turning the car on just so the battery turned on and I played some music through my iphone. I did this for about 10 minutes and I was fiddling around with the bass setup and reverse speaker and or normal speaker, and the hertz from 50 hertz to 125 hertz. The next day I did the same thing and when you turn the car off you have the option of taking off the head unit (It slides right off) So I figured sure Ill take it off and put it in the glovebox, So I did that and locked the glovebox. Next day I go to get plates to register the car, and the car wouldnt start, my dad immediately told me that I shouldnt have sit in the car and played music. So we charge up the car with a battery charger, the black terminal (negative) had a bunch of dirty stuff (I'm guessing corrosion) around it so we cleaned it up with some terminal battery cleaning tool. Then it started up fine. So we took it for a ride and I plugged on the radio when the car was off, then I noticed shortly after it said Change alternator error on the dash and it was dimmed. So I pulled over switch seats with my dad and he drove it back home, on the way home the setup on my head unit was going crazy switching bass from -6 to +6 without anybody touching it, So I slid it right off and put it in the glove compartment. Came back home charged it, and then took it for another ride without the radio. Please help me, Do I need a new battery or a new alternator, or maybe should I get it checked out first by a trusted mechanic?

Get the battery tested first.

Auto parts stores will usually test your battery for free. Just drive the car to the auto parts store and ask them to test the battery and the charging system.

If the battery is bad, you can get a new one right then. If the alternator is not charging, look at the fuse panel on top of the battery. The alternator wire is the black wire closest to the engine. A bad wire will melt the fuse panel and the copper wire in the terminal end of the wire, at the fuse panel, will appear gray, green, or black instead of the normal copper color. If that is the case, replace the alternator harness and the fuse panel with new parts from the dealer.

The radio going crazy is probably due to low or irregular voltage to the radio, from a bad battery or charging system. Or a bad ground for the radio.

Get the battery and charging system checked out first.

Could not follow?
When the car did not start, it could be from draining the battery with the radio, but could also just have been dirty terminals.

So now that it is starting, why are you concerned?
The battery is only a concern if it won't start.
The dash change alternator error is not possible with the car off.
The head unit going crazy can't have anything to do with the battery.
More likely you slid the head off while it was still on, and confused it.
But you might also have the radio wired wrong, where constant power to the radio is being fed back to the ignition or something?

It is not clear what is the concern or symptoms.
Don't have your battery checked, because they always say it failed, unless they would have to warranty it. If it cranks, the battery is good enough.