How can I save and print out iPhone text messages for court?

There's no Print command in the Messages app but you can copy messages into an email message and print or save that. You can also print a message chat using one of several third-party apps for Windows or Mac.

This article may help:

https://www.businessinsider.com/guides/tech/how-to-print-text-messages-from-iphone

You can print individual screenshots of the conversation.