Greetings Galloglac,
Yes. You are able to use Wi-Fi and Bluetooth while in Airplane Mode and you can find more details about that here:
Use Airplane Mode on your iPhone, iPad, iPod touch, and Apple Watch
Next, we suggest completing the following steps to get Wi-Fi Calling working as expected:
"If Wi-Fi Calling isn't working
If you can't turn on or use Wi-Fi Calling, make sure that your carrier offers Wi-Fi Callingand that your devices have the latest software.
If you're unable to turn on or use Wi-Fi Calling, your device software is up to date, and your carrier supports Wi-Fi Calling, contact your carrier.
If you contacted your carrier and can't turn on Wi-Fi Calling or make a Wi-Fi call, follow these steps. Wait two minutes before you go from one step to the next.
- Go to Settings > Phone > Wi-Fi Calling and make sure that Wi-Fi Calling is on.
- Restart your iPhone.
- Connect to a different Wi-Fi network. Not all Wi-Fi networks work with Wi-Fi Calling.
- Turn Wi-Fi Calling off and then on again.
- Go to Settings > General > Transfer or Reset iPhone > Reset.
- Tap Reset Network Settings."
More info here: Make a call with Wi-Fi Calling
We hope this helps.
Take care.