Cache is essentially RAM, but more accessible. It's just data that gets stored in memory for future use. I don't know if this has been suggested, but you can try navigating to your usage settings and examining how much data each application has accumulated (cache). When I notice an app using an abnormally large amount of data, I just delete the app and reinstall it (probably not the most effective/efficient method, and it's crude, but it works )
I checked out DiskAid and it's pretty good, but it seems to have problems with the pictures in the messages, I don't know why. I also checked out iExplorer, of which I know that it's a trusted application and I could actually see the pictures here, but it's more expensive. Both of these options would cost me at least two months to get the money for. DiskAid is cheaper but I'm afraid it won't work the way I want it.
I don't have an iPhone, but surely you can download an app that can explore your phone (I use X-Plore on Android) and copy the messages to an SD card? Then use an SD card adapter to put it in your PC. Copy, paste, messages saved. I really don't know; I'd try that, at least.
I was looking for something similar for a friend recently but we were trying to move pictures. Supposedly we could have used iTunes to do it but all the instructions we found were for different iTunes versions or iDevices and we finally gave up. In addition to DiskAid, there were two other apps we saw while looking that might work for you: CopyTrans and Dr.Fone. There seems to be a lot of different ways people are doing what you are trying to do but every app is a little different and may or may not have the exact features you want. You are probably going to have to try a few out before you find one that fits your needs.
