Repetitive beeping, occasional dying, and a not so smart key

After browsing previous posts, I'm hoping to get some specific input on my 2008. About every other time I power off the car, the interior beeps repeatedly once I open the door as if I had left the key fob in. Around the same time I noticed my car kept dying in the garage, but only on the occasions when it beeps without reason (nothing is left on). If I cycle on and off, and change the gears a couple times, eventually I can turn it off and open the door with no beeps and the car wont die, even if it sits for a week. I haven't checked the voltage on the 12V although that's my next step.

Also, half of the times it gives me the beeping trouble (so about a quarter of the time overall) the display gives me the red triangle and a message about the locking mechanism and parking (sorry I don't remember it verbatim).

Another abnormality is that the smart key system no longer works. The battery in the fob is good and I can lock and unlock it with the buttons, but I can't unlock the car by putting my hand under the handle and the fob must now always be in the ignition. I don't know if they're related but all these problems surfaced around the same time.

Thanks in advance for any help!