Hello!
Checking cellular data in general and for FaceTime was great. Since they are both enabled and you still can't connect to FaceTime, try following If you can't make a FaceTime call on your iPhone, iPad, or iPod touch - Apple Support
Resetting network settings may help, but keep in mind you will need to re add your WIFI networks. and your device will restart.
If the issue is still not resolved, I would recommend backing up your device to iCloud or iTunes and restoring as new to isolate the issue.
If you set up your iPhone as new and you can FaceTime over cellular, then you can try restoring from your backup to retrieve your stuff. If the issue comes back once you restored your backup, that means that you should set up the device as new and manually bring over your stuff as there may be something on your actual device causing the issue.
I hope this helps!