Is there an issue with logging into FaceTime or iMessage on ipad4?

FaceTime and iMessage continue to be functional with older versions of iOS. Perhaps this support page will be helpful with troubleshooting the problem:

If you get an error when trying to activate iMessage or FaceTime – Apple Support

The probable issue is that an iPad 4 can only be updated to version 10.3.3. Newer versions of Face Time and iMessage may require newer versions of the OS.