How can I backup or archive my iPhone messages?
To keep old messages for posterity, I would perform a backup and then rename it so that it does not get overwritten. A quick google search will give plenty of instructions.

As regards to restoring individual messages to your phone, I don't know that it's possible. There are certainly a number of non-free desktop apps for both PC/Mac to extract and view items from backups, again a google search will give you what you need.