The pictures of it, and you saying you had to remove acid corrosion from it, tells me your batt is old. Batts wear out, their internal resistance increases as the plates oxidize. The older it is, the more its oxidized (obviously). And, the more current you pass through it (like adding a big aftermarket stereo), the faster it oxidizes. My guess is your batt needs replacing. A worn out batt does not explain the voltage spike however, just an additional bit of information for you.
Buy a DMM.
Replace the batt.
Do the big three.
Report back to us.
In that order.
Do not skip step 1.
If all else fails, you do not have to go buy an amp from fry's just to get them to diagnose your wiring issue. You should have a reputable shop somewhere locally that would look your system over, for a reasonable fee. If a shop says they wont unless you buy something from them, then you know that shop sucks.