Making calls from my iPad

I forgot about being signed into FaceTime as well.

Make and receive calls on your Mac, iPad, or iPod touch - Apple Support

With regard to Messages, try signing out of iMessages, restart your iPad and then sign in again and see if you can send a text.

Have you tried using another WiFi network to see what happens? Another thing that you could try is a forced restart. I use this all the time when weird things happen on my iPad and iPhone and nothing else works. Apple recommends that you only do this if the device is frozen, but it has cured some really hinky issues on my devices.

• iPad models with Face ID: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Then press and hold the Power button until the device restarts.
• iPad with Home button, iPhone 6s or earlier, and iPod touch (6th generation) or earlier: Press and hold both the Home and the Top (or Side) buttons until you see the Apple logo.

You cannot make a phone call on an iPad without having an iPhone, being signed into iCloud on both devices, being on the same WiFi network and having the settings on the phone to allow calls on other devices. Do you meet all of that criteria?