iPad Pro 9.7” - defective embedded sim?

I bought a new 9.7” iPad (wi-fi + cellular) a few days ago, added to existing AT&T service plan, and have had repeated problems getting cellular data service to work. My cell phone gets AT&T signal with no problem.

I was on phone for a long time with AT&T specialized tech support before they could get iPad’s cellular data service set up and working initially. Now sometimes works, but more often iPad says either “NO SIM” or ”no service.”

Turning iPad off and on again worked a couple of times, and updating to iOS 11 (latest version) worked once, but fix never lasted long and now have same problem again and can‘t fix it.

1. Is there anything more I can do, or is embedded sim defective, meaning I have to return the iPad?

2. Are defective embedded sims a common, known problem with the new 9.7” iPad, or did I just get a lemon?

3. Finally, if I have return, how can I “erase” or “remove” any personal info that may now be stored on the embedded sim or iPad first, so I don’t risk others getting access to my info?

Thanks