If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad to non-Apple devices, you must explicitly enable Text Message Forwarding for your iPad on your iPhone...
On your iPhone:
Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.
Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:
Settings > [Your Name / AppleID] > Messages - set to ON
For Cellular Calls from iPad, if your both your Cellular Carrier and your calling plan support WiFi Calling, your iPad can make and receive calls independently of the iPhone - even when the iPhone is switched off, elsewhere, or using a different WiFi network. Not all carriers support full WiFi calling.
The settings that you need to change/verify on your iPhone and iPad are:
On your iPhone
Settings > Mobile Data >WiFi Calling >
- WiFi Calling on This iPhone - set to ON
- Add WiFi Calling for Other Devices - set to ON
Settings > Mobile Data > Calls on Other Devices >
- Allow Calls on Other Devices - set to ON
- [Allow Calls On] - explicitly enable your new iPad from the list of devices.
On your iPad
Settings > FaceTime > Calls from iPhone > Calls from iPhone - set to ON