Problems after rooting with TWRP and SuperSU
In case anyone else has the same issue, I managed to solve the problem. 

I unrooted the phone using the option in SuperSU, and then flashed the device with the stock firmware using Odin. 

This fixed all the problems, and allowed me to successfully connect the phone to the PC via USB.  

It turns out SuperSU was problematic, and that Magisk is a better solution for this particular firmware. 

So I placed the latest Magisk build on the phone via USB, then used Odin to put TWRP back on the device. Then, from the TWRP Recovery menu, I installed Magisk. 

After this, I installed Magisk Manager from GitHub. 

The phone was successfully rooted after this point, and all functions are working properly.