mamasaurus

Hi folks - Thanks in advance.
2005 RX330 is doing the following:

-Occasionally locks the back doors so they can't be opened from inside. Child locks are not engaged. Can't reproduce for the dealer so they think I'm bonkers.

-Passive alarm malfunction - If I walk away, close the doors and forget to lock the doors, it used to lock them. Now the doors remain unlocked but the alarm arms. I can open the doors easily but then the alarm sounds.

-Headlights didn't turn off automagically overnight. AAA guy who jumped the battery thinks I'm bonkers. He says, "when they're in the 'on'" position they will stay on until the battery drains." I have driven this car for ten years. That is not the case. (right?) I assume I forgot to lock the doors with the key fob, so the lights stayed on. Possible? Shouldn't the automatic passive arm/lock/turn lights off have covered that for me? This isn't 1986.

I have to believe these issues are related…or I'm bonkers. Help!