1) A burned out bulb in the signal circuit will cause rapid light blinking. Replace all burned out exterior bulbs. Go to Pepboys for bulbs.
2) Replace burned bulbs.
4) Since you can easily rise & lower the mast, sound like a broken plastic mast winding cable. Clear the antenna motor mechanism of broken pieces and replace with new mast.
5) Hard to believe 155K belt isn't worn, sound like the seller pulled a fast excuse on you. My 150K belt was quite worn when replaced.
The name that comes to mind is "Lexokico" for your Lex-BMW hybrid ride.
Welcome the the club and enjoy your "new" car!