The first pic looks like a connection for a V1.
BMW makes aux-in adaptors for some units, but I am not sure what radios it works with. There are also aftermarket solutions (dice, etc, check BSW's website). I would take that ugly mount out and place the connections in a eurotray, which is a part you can get from a delaer and replaces cup holders, or you can go to the glove box.
As far as audio cutting off, someone has to troubleshoot to figure out what the problem is. Could be head unit, wiring, amp, shorted speaker.