My server ip address has changed. I have moved the search engine to a new machine. Do I need to purchase a new license and should I request an unlock key again?

You do not need to purchase a new license. You must have a number of licenses equal the number of servers you run the search engine on.

When your IP configuration changes you should request a new certificate and mention in the comments line that you are moving servers or your network configuration has changed. Do provide licensing information such as Kagi transaction number. We will issue as many new certificates as needed free of charge.