Q: imessenger

No. This is a carrier function.

It does not do any good to block them from the carrier.  There HAS to be a way to blocking specific people without blocking everyone.

If your carrier offers it, then blocking that person will not block everyone.

If you know this person, report the harassment to the local authorities.

You were not specific in your OP whether it was iMessage, or SMS that the person was sending. Short of deactivating iMessage, there is no way that I know of blocking specific users.

No. Beacuse iMessage still will connect using the wireless network to access the Internet.

Be aware that imessage also uses your iCloud account so that others can reach you using your xxx@icloud.com address (and xxxx@me.com etc).

So when you get your new number, make sure that ONLY your number is selected in the iMessage prefrences. That way the person will NOT be able to contact you using you icloud/Apple ID.

Good luck.