I don't really know anything about your car, but I can comment on how mine works.
Every day, at 2pm, my traction battery charges the 12V battery. (While this is happening, there is a quiet beeping sound from the car interior).
This is because I have a version of the PHEV that has wifi connectivity, dashboard computer (MMCS) etc. (according to the dealer).
Other than that, the 12V battery charges up every time I turn the car on.
The engine is not used to charge this battery, except...
... If the traction battery has been run down and the engine starts to charge the traction battery, it's possible for the 12V battery to charge at the same time.
So the only time it would be necessary to use 'Charge Mode' would be if the traction battery is low.
If I had to leave my car for long periods (i.e. months) I'd leave it at home, plugged in, with the timer set to charge the car for half an hour, one day per week.
This may not be necessary, as my car turns off the wifi if the car has no activity for three days (most likely to conserve the 12V battery).
Unfortunately, I don't know how the burglar alarms work, what their drain is, etc.
My understanding is that some vehicles have an alarm supplied by Mitsubishi, which is integrated into the vehicle's systems, while others have after-market models supplied by dealerships.
I've heard that alarms which use proximity sensors to read a card held by the user, use more power when the vehicle is powered down, but I don't know if that is true.
Mine has a dashcam fitted, and that has a separate battery power supply on the recommendation of the firm that installed it. They held the opinion that a dashcam in 'parking mode' could exhaust the small 12V battery in the PHEV very easily.
Hopefully the above is of some assistance.