Hang on, slow down. Remove your email account. Restart the device and then add the account back.
See what happens then. You've said you've done, "everything", did you happen to reset to factory?
If my initial test fails, reset to factory, connect your account and test Contacts. DON'T add apps etc., prior to testing Contacts.
It could well be a setting, app or widget causing the weird issue. Hence my ideas.