Are NXT messages stored on the blockchain and are they encrypted or publicly viewable? Are nxt messages stored on the blockchain?

What is the character limit on these messages?

And are the messages encrypted or publically viewable? If they are public, is there a site to just view all the messages sent?
Yes they are stored in the blockchain.

They are limited to 1000 characters.

They do not have encryption built in, but encryption can be built on top. You can view the last 300 messages here. You can also use that site to browse through blocks and see the messages embedded in each one.