Well for starters that looks like 8 gauge maybe 4 gauge which is not big enough for the amperage you are pulling.
When the subs were cutting in and out, your amp was going into low voltage protection. It would shut off until the voltage returned. Then start again.
You need a better battery for sure. And a high output alt.
Any shop saying big 3 is enough to push a solid 2k of power is full of it.
I would go back there and tell them to take all the crap they sold you back and give you full refund, and to replace all the wiring they fried.
Go find a new store.
Hopefully your alternator is not fried.....