2008 prius w/ proximity sensor & ac problems

Hey, I'm excited to have a new hand-me-down 2008 prius from my mother but it has a few quirks that I hope I can fix.

1) the proximity sensor on the key fob isn't working. It doesn't work to open any of the doors. The lock and unlock keys on the fob work just fine and I can start the car by inserting the fob. However, a year ago the proximity sensor was working and it was lovely to be able to open and start the car with the keys in my pocket the whole time. Also it was nice to never be able to lock my keys in the card by accident.

I believe my mom has gotten a new key made for the car since it was last working because she lost the last one. (I only have one fob for the car because she lost one of the two originals previously. But I have had a copy of the emergency mechanical key made so I can enter the car if I lock the fob inside). She insists that the Toyota service people tried to troubleshoot the proximity issue but weren't able to resolve it and encouraged me to drop it. I don't exactly trust her understanding of anything technical so I've been looking around here for possible causes. I tried replacing the fob battery just in case. And I tried pushing the KEY button under the steering wheel. Some others indicated it might be something wonky with the 12v battery -- but I just ran the diagnostic check on that (by holding the DISPLAY button and turning the lights on/off 3 times) and the voltage is reading at 12.1 volts so that seems to be fine. Any other ideas?

2) I've been having some A/C issues. A couple years ago there were problems with the AC not running cold but my mom has since has the AC serviced and freon added. But today there was an issue where I was parked and the A/C wouldn't blow cold air despite cranking it up to LO and MAX. It had been working fine while driving. I turned the car off and on but it still wouldn't catch. I drove it for a short while and it continued to blow hot air. Ten minutes later when I started it up it was still blowing hot air, but then when I was sitting at a stop light, I heard the engine cut in and it started blowing cold air right away. It makes sense to me that the AC wouldnt work on the battery alone but I don't understand why the system wouldnt have automatically switched to gas sooner than it did. It isn't a big deal but am including it in case it might be symptomatic of a bigger issue.

If any of these issues sound familiar to something you've been through, I'd love your insight and feedback!

Thank you!

 

135,000 miles. And the current fob is a replacement as my mom lost the two originals. I think poking around this forum that I finally understand that although the car has SKS (and the original fobs worked), the replacement fob my mom purchased from the dealer isn't capable of working with SKS (it has a black back compared to a silver back?). So I'm not holding my breath to get that to work anymore.

As for the A/C blip, I'll keep and eye on it and bring it in if it continues to act up.

Thanks so much for the response!