It is possible to have a battery problem that brings up spurious codes. I have had most of your list except for the wiper problems. I did not have to replace the battery because it was partially flat when it happened to me twice in 2 weeks.
The most sensible route (I did this 2 years ago) is to eliminate the battery first before spending any more money. I would recommend you seriously consider purchasing a CTEK MXS 5.0 battery charger (Advanced charging with temperature compensation) and if your are able charge the battery for at least 48 hours, and take it from there. I am surprised the dealer did not recommend that first.
Here is the information:
MXS5.0 Advanced all round charger
The MXS 5.0 is an advanced microprocessor controlled battery charger with automatic temperature compensation built in providing unrivalled performance on batteries from 1.2Ah up to 110Ah. The MXS5.0 solves a broad range of battery problems and is the ideal charger for the user with high demands. Features of the MXS 5.0 include diagnosis of battery condition to establish if it can receive and retain charge, patented automatic desulphation programme and a special reconditioning function that will revive and restore deeply discharged and stratified batteries. AGM mode is perfect for maximising performance and life of most Stop-Start batteries. The built in temperature compensation ensures ideal charging performance even in the most extreme conditions. Patented Float/Pulse maintenance makes the MXS 5.0 ideal for long-term maintenance.
UK Amazon link (naturally yours will be a different URL):
https://www.amazon.co.uk/CTEK-MXS-5-.../dp/B00FC42HAA
Note. CTEK make a charger for BMW. I suggest you do not bother with it, because it is only a trickle charger.