1) The owner's manual says plug in when you don't drive, so plug in while you are away for 1 month is the correct action.
2) The App/Charging screen allows to charge anywhere from 50 to 90% for daily use and above 90% for a long trip as needed, so in your case, from 50 to 90% because you are not using the car right away for a long trip but 1 month later.
Different people would give you different numbers anywhere from 50 to 90% and they are all correct because their numbers are within the range given by Tesla.
Some people believe sub 90% will prolong your battery life while Service Center wants you to set it at 90% and don't have to worry about the different numbers.
I haven't seen any documentation saying if you set at 80% instead of 90%, it will prolong your battery to an additional 3 days or 10 miles or whatever the numbers are so I just do what Service Center says.
3) Since you can plug your cable to charge your car and keep the wifi on, those are good things in case you need to update the firmware when you are away or access your car for your friends and family to work on it.
4) Your 12V battery is charged from your main battery pack. As long as your main battery pack is plugged in, your 12V is safe. If your main battery pack is not plugged in and it starts to deplete, it would no longer charger your 12V and since 12V is lead-acid so it hates low charge and at risk of dying if you don't plug your Tesla to a charger.
I left my model X for a month last year. I left it with 60% charge, plugged in, and the charge setpoint at 50%. All went well. Here was the progression of the battery charge:
Day 0 - 60%
Day 7 - 52% (software update)
Day 14 - 47% and it charged to 50%
Day 20 - 48% and it charged to 50% (also software update)
Day 25 - 47% when I arrived home
I did not check it at all via the Tesla app, except to authorize 2 software updates I was notified of. I know the intermediate states of charge and charging behavior from Teslafi.
Does the X top off charge when plugged in if a set charge of 50% or 60% falls over time? If so, at what threshold drop does the X start pulling power from the charger again to top off at the set limit?
Meaning will the X know it lost some juice and look to top off juice again without needing to mess with the Tesla App?