Antitheft lockout, multiple alarms, starter battery drain

[MarthaT]

My 2010 Milan Hybrid has had an undiagnosable problem (possibly electrical) for more than two years. 

Intermittent multiple alarm problems began in late 2019. The alarms were obviously false. Here is what happened. Car started normally. Within a couple blocks, alarms began:

• Blind Spot System Fault,
• Cross Traffic System Fault, 
• Stop Safely Now with red triangle,
• Service Advancetrac,
• Check Charging System,
• High Engine Temperature,
• High Motor Temperature,
• Fuel Level Low,
• (And, after several minutes) Tire Pressure Monitor Fault.

The (original) 12-bolt battery was replaced and that fixed it for a short while. I was told to drive more to charge the battery, which made sense, since I had not been driving much due to the pandemic. An hour of highway driving would give me just 2-3 days of normal operation.

Last year, a new symptom has appeared: I often cannot start the car due to an antitheft lockout. Replacing the key fob batteries had no effect. Again, I suspect this is due to low 12-volt battery charge. 

More than once, I have had wiring checked out for binding, current leaks, or other problems with nothing found. I am assured the 12-volt battery is fine.

I left it with a Lincoln dealer for TWO WEEKS and they found nothing (the hourlong drive to dealer had apparently charged up the battery).

Last fall, I finally got a trickle charger and plugged it in every night. That dealt with the symptoms for several months. Now, despite nightly charging, it is only good for two starts each day. On the third try, I get the antitheft lockout, so no en-route errand-running is possible. 

Also now, as soon as I start and begin to back out of the garage, I get Cross Traffic System Fault and Check Rear Park Aid notices that stay on the entire time the car is in use. Cross Traffic amber lights DO both come on appropriately, but the rear park assist alarm no longer sounds. Posts here lead me to believe that is a problem with the little speaker for it rather than the sensors. (I have no one to listen for the clicking in reverse.) That seems unrelated to whatever the major problem is.

Possible clues:

• When I drove at highway speeds to recharge it, often all the alarms would stop except the Blind Spot  and Cross Traffic System Faults, and the amber lights in the side-view mirrors would stay lit until I shut the car down.
• Once, a car pulled out in front of me, causing me to slam on the brakes, and all the alarms shut off.
• In recent years, in cold weather, the rear defrost and seat heaters would occasionally just not work.
• On 8 Apr 21, I did disconnect a phone charger I had had plugged into the dash power source (and got weeks of normal operation before the warning-light circus began again on May 25). This long period of normal operation ended right after I had used the seat heater for the first time in ages.
• A few months before the alarms began, I had had the driver-side rearview mirror replaced.

Any ideas? Honestly, I am ready to buy a Chevy Bolt, after more than 40 years of Ford vehicles.