iMessage issue

I convinced my wife to switch to iPhone (all her previous phones were android) anyways iMessage isnt working properly 80% of the time when she messages me she says they go through as regular text messages... We have tried

1.restore
2. Signing in and out of iMessage
3. Removing the 2 addresses (email and phone) where she can be reached via iMessage and just left her phone number
4. Signed in and out of the App Store
What else can we do?

Also there is a delay sometimes of about a half hour or more with her receiving my iMessages (her cellular data is turned on)

 

Thank you, called the provider and they said everything is as it should be. But resetting the network settings seemed to work *knock on wood* they are coming through instantly hopefully it stays this way