2001 BMW M5 My battery arched and now I have electrical pro

My alarm went off one day and wouldnt turn off the only way I could get the thing to stop screeming was to disconnect the battery. The alarm stoped and I hooked the battery up and went to bed the next morning I tried to start the care all it did was make a noise like the batery died or a loose terminal checked the connections and realized the terminal had broken in side the battery case.(New Battery time) Installed the battery and the radio plays for 2.5 minuets and shuts off you can hit the button and it plays again but 2 min later its off again.I wasn't home so on my way home the car drove great parked the car and the next day it runs like ish. I have codes on the dash and he ac stoped working any ideas?