How do you set a mailbox to send email but not to receive in Exchange 2007?

You could place delivery restrictions on the mailbox by accepting mail from only a special account or an admin etc... ( This is exch 2010 doc, but still applies)http://technet.microsoft.com/en-us/library/bb124405.aspx#MDRestrictionsOr create a Hub tranport rule:http://technet.microsoft.com/en-us/library/bb421708(EXCHG.80).aspxHow you want to enforce this really depends on what you are trying to prevent. Message delivery restrictions will generate a NDR and will apply to all senders, internal and external. A Hub Transport rule can be applied to certain conditions and the message can simply be dropped.

Basically, this is an unmonitored mailbox and dont want to allow incoming email. Also, is there a way to have the reply not be an NDR but a message that says this mailbox is not monitored, etc.....

Check out the Hub Transport rules or use an Outlook rule. Note that auto-replies are a bad idea. They can lead to mail loops and responding to spoofed messages is a good way to get blacklisted if they are allowed to the internet.