I've been struggling with the headphone output. When using my phone through an aux jack in the car. The phone thinks it is plugged into a headset with a Mic. People I call can't hear me. And I can not use my voice to enter text without unplugging the aux cable. Very hazardous while driving.
A separate issue I am now having is when using a standard tip ring sleeve head set. It seems that I'm listening to a sound that is the result of connecting the positive leads of both drivers to the left positive amp out, and the negative leads of both drivers into the right negative amp out. This results in a sound that is echoey and mono.
I'll try to address your questions in reverse order:
Are you using some form of case? Some cases do not provide enough clearance such that you can plug in your device properly.
Have you tried another "standard tip ring/sleeve headset". You want to make sure your audio jack is not defective. Again, try using a different set of earbuds without a case. The one you are currently using may not be working correctly. It's possible.
For both of the above tests, I would download Stereo Test to individually test both channels:
In the end - if your input still "mixes" left and right channels providing you a mono audio out, either you'll have to get the phone serviced, or go Bluetooth.
I personally would not be using an AUX jack in the car, and for that matter, on these high-end phones, I avoid putting needless cycles on the audio connector. Instead, I use BlueTooth. You can get a very inexpensive A2DP receiver and plug that into your radio. Search for A2DP bluetooth adapter on Amazon. They are cheap. Then stream your audio to your radio. Only connect the audio profile so you can use another BT headset for calls.
Now if you absolutely think you need to make and receive calls while driving (???) then get a BT Headset, and use that to answer calls. Don't pick up your phone. Keep both of your hands on the wheel. It's safer.
Another possibility, get a device that will act both as an A2DP receiver and has a microphone for making calls that can be mounted on the dash and plug that into the radio. Use both Audio and Phone profiles.
Consider - it's best to avoid using your phone while actively (?) engaged in driving. People do it all the time I know, but their driving skills, their awareness of surroundings, and their reaction times are worse when on the phone. You are a safer driver both to yourself, and to your fellow drivers if you just aren't on the phone.
I don't mean to lecture. It's just a fact.