To resolve the problem with your caller ID:
Reset your iPhone - press and hold Home and Power button simultaneously, until the Apple logo appears. Let go of both, your device will power up on it's own.
Reset all Settings: go to Settings - General - Reset - Reset all Settings. This will set back all your settings to default, and you'll have to look at everything again, to choose what you prefer.
Resetting all settings could also help with your problem with vibration.
Restore your iPhone. Make sure there's a most recent backup (iCloud or iTunes), and restore your device via iTunes. Restore from the backup afterwards.
If restoring from the backup reproduces the same problem, set up your device as new.
If all this doesn't help, contact your carrier. The reason of your issue could also be a fault on their part.