Can a Bluetooth showed connected be a different one

Yes, I once was trying to connect my phone to my airpods but they were not charged up so my phone was trying to connect to my next door neighbors phone.

Maybe but unlikely. Your car wasn't trying to connect, it connected which means it was paired before. When it connected, the person who was talking would have lost the other person's voice and might have hung up thinking they had lost the connection. Look at your car radio and see what devices are allowed to connect. Delete any that you don't recognize or no longer use. I recommend giving your phones real names as well, not just iPhone 10 or Samsung S21, but "Joe's iPhone" or "Mary's Samsung" so you won't run into other devices with the same name.

If your device is setup to automatically connect, and the other device is setup to automatically receive. You saw your wifes phone because it was probably connected. If a person had your wife phone bluetooth credentials they could connect to the deviceas if it was paired already. That would take programming.

Then there is bluetooth hacking as well. You could pick up on data signals.

Finally in terms of phone information, if you had the right tech and decoders you could pick up messages, or even whole conversations. Like when a police-car roles by ( around 30-70 feet away ) and I am on the phone I could hear the entire police radio call. By that logic they should be able to pick up on my device and my conversation.

In fact if you had the proper radio equipment, frequencies, power, and antenna you should be able to pick up peoples conversation. Even via using a portable dish. The same could be said about a big dish on a house. Not only cable channels but radio stations and peoples conversations nearby.

My dad works ( worked ) in telecommunications and show me using his equipment ( he has for work that is his property ) and was able to intercept peoples conversations just by tapping into the phone-wire. So when you see a repair man with a specific device in hand chances are they were able to listen to any communications going through the wire ( no different then a radio line ).

Point being is that communications via Bluetooth was funny but now is not really a big deal. Just bare in mind the bluetooth is not secure %100 and your allowing for "listening" from other devices. If a person was intelligent enough ( or had the spare time ) they could use the bluetooth for a variety of things.