How do I transfer readable text messages from my iphone 7 plus to my pc? I would like to save entire conversations. I don't see the option in itunes. There seems to be 3rd party purchase apps but I'm not sure how secure this option is?

There is nothing inherently insecure about an app simply because Apple is not the developer. If the app has a remote storage or networking function, you do have to be careful. That's why Facebook and anything by Google represent security concerns. Your cell phone carrier sells collects and sells far more information about you than probably anyone yet no one ever seems terribly concerned about that.

TouchCopy copies the data from your phone to your computer. The data is never leaving your control. I suspect it would be pretty easy to verify this by disconnecting all of your devices from the internet before beginning the transfer.

TouchCopy (Mac & Windows) gets recommended frequently. It's not free but I've never heard anything negative about it here. I don't see where security is a concern as the messages are being transferred directly from your phone to your computer.

Best of luck!