How can I print all texts from a contact to my iPhone?

If you have a Mac it can be done.

• Text Message Forwarding to mac (Use Same Apple ID)
• On Mac Open iMessage > Select the Message Thread > File > Print > Save as PDF

Short of doing individual screen prints, you need a 3rd party app for your computer. Three that can do this on Windows and Mac are iMazing, TouchCopy, and PhoneView (Mac only).