IPad – iMessage appears to be blocked, but FaceTime rings

First, the best advice for dealing with a hungry troll: don't feed him.

Ignore this guy, and he will quickly get bored and move on.

If your device runs iOS 7, you can block FaceTime and messages from known addresses that disturb you.

However, if unknown individuals are bothering you with frequent iMessage text messages, you can adjust your Notification settings to ensure that you are not interrupted with alerts when messages from unknown contacts are received (the messages will still be waiting for you in the Messages app, but you will not receive pop-up or banner notifications about them).

To disable notifications for iMessages from unknown contacts, go to the Settings app, then Notifications, then Messages, then scroll down to the "Show iMessage Alerts From" and select My Contacts Only.

Then, ensure that the person who is harassing you via iMessages is NOT in your Contacts. You should no longer receive alerts about his messages (but they will still be received in the Messages app).

Note that this also means that you will not receive notifications about messages received from ANY unknown contacts - you will only receive notifications about messages received from phone numbers or email addresses that are stored in your Contacts. So, be sure to check your Messages app regularly to see if you've received any messages from people not in your Contacts list that you WANT to hear from.

No. Blocking a number will block it for normal calls, FaceTime and FaceTime audio.

You might have to pay attention to the details though to fully block someone. Anyone using FaceTime has an AppleID so you'd want to block the Apple ID (usually it's an email) and possibly also block the associated cellular number(s) since you can attach several phone numbers to one Apple ID.