No real need to change the system, just need to do it the way that Tesla expected you to do this.
In that situation, the passenger simple touches the main screen after the door closes and the screen turns off. When they do that, the screen, the HVAC, and the "radio" all turn back on. There is some form of timeout on this wakeup, maybe 30 minutes. If you're away from the car longer than that, they'll need to touch the screen again to wake up the screen again. No biggie.
As for the alarm going off, I'm not quite certain about that. I myself haven't noticed that, but I generally don't leave passengers in the car alone. Did you passenger use the manual/emergency release (pull lever) instead of the regular push button release? I could see that as triggering the alarm. If they used the push button to open the door, you could have them try again, but press the unlock button (the padlock) on the screen first to unlock the door. This sounds like an interaction with the alarm that is part of Sentry Mode. You could also try turning off Sentry Mode after putting the car in park if you plan on leaving a passenger in the car.
Note that leaving your key card inside the car won't do anything. The range on the key card is rated in inches. Its general location in the car is not used as a determining factor to lock/unlock the doors. The only place the key card is read is when it is held to the driver's side B pillar or the center console near the drink holders. Leaving your cell phone programmed as a key in the car with your passenger would keep the doors from locking and possibly the alarm triggering.
Just a couple things to try.