Hello Marry mini,
Thank you for the details of the issue you are experiencing with iMessage on your iPad and iPhone.
It sounds like you prefer not to receive messages on your iPad, so I recommend leaving iMessage off in Settings > Messages on the iPad.
iPad User Guide - Messages settings
http://help.apple.com/ipad/7/#/iPad99acb5bb
Next, I recommend the following steps to troubleshoot iMessage on your iPhone:
To resolve issues with sending and receiving iMessages, follow these steps first
- Check iMessage system status for current service issues.
- Go to Settings > Messages > Send & Receive and make sure that you have registered iMessage with your phone number or Apple ID and that you have selected iMessage for use. Learn more about troubleshooting iMessage registration if the phone number or Apple ID isn't available for use.
- Open Safari and navigate to www.apple.com to verify data connectivity. Learn more about troubleshootingcellular data or a Wi-Fi connection if a data connection isn't available.
- iMessage over cellular data might not be available while on a call. Only 3G and faster GSM networks support simultaneous data and voice calls. Learn more about which network your phone supports. Go to Settings > Wi-Fi and turn Wi-Fi on to use iMessage while on a call if your network doesn't support simultaneous data and voice calls.
- Restart your device.
- Tap Settings > General > Reset > Reset Network Settings on your iPhone.
If you are still unable to send or receive an iMessage, follow these steps
- Make sure that the contact trying to message you isn't blocked in Settings > Messages > Blocked.
- Verify that the contact you are attempting to send a message to is registered with iMessage.
- If the issue occurs with a specific contact or contacts, back up or forward important messages and delete your current messaging threads with the contact. Create a new message to the contact and try again.
- If the issue occurs with a specific contact or contacts, delete and re-create the contact in the Contacts application. Create a new message to the newly created contact and try again.
- Back up and restore your device as new.
iOS: Troubleshooting Messages
http://support.apple.com/kb/TS2755
Additionally, you mentioned your contacts' names are missing. You may want to check in Settings > iCloud and verify that you are signed into iCloud and have Contacts enabled there:
iCloud: Change iCloud feature settings
http://support.apple.com/kb/PH2613
Thank you for using Apple Support Communities.
Best,
Sheila M.