Q: Does phone calls on my iPad use data

Phone calls on your iPad?  Your iPad is not a cellular telephone.  It cannot by itself send or receive cellular telephone calls or text messages.

So perhaps you're using Skype.   (Your iPad could use FaceTime, but you say it's off.)

If you have an iPhone you could have Continuity turned on which will allow you to answer phone calls on your iPad.

Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support

You said that you don't have an iPhone and you don't use Facetime. That really only leaves an app like Skype where this could be happening. Has anybody else ever installed apps on your iPad?

Missed the part about the iPhone, my apologies. Are you around someone with an iPhone that may have used your iPad when this happens? Can you you do a screen capture that next time it occurs? And finally, is your iPad jailbroken?