I do not have a X-T5, but I am wondering if maybe you have activated the Dual Display setup: https://jmpeltier.com/fujifilm-manual-focus-assist-modes/ scroll down to the Dual Display section. It does use a split screen approach and will let you also use focus peak mode and then go back to split screen after a restart, at least that is what the article implies anyway.

Something to do with custom settings perhaps - but I can't figure out the exact configuration that would cause this - do you use custom settings and do you have different focus assist options with different custom settings?

I honestly have no idea. I hope our guru @Greybeard or @jerryy will chime in with something. 

I don’t have that camera, but when there are various colours of light in the scene (like a sunset or various indoor lights) the Auto WB can be thrown off, that is normal I think. In these cases I use a fixed WB like “daylight” or “cloudy” or a Kelvin value. Also, look at Natural Live View. You can map that to a button and switch easily between that and your film simulation. At least on the X-T5 you can and I presume on your camera too. 

The usual route would be asking you which firmware version, what type of card, what settings (try a reset) etc. But there could be a bad batch of cameras, maybe a supplier delivered a bad batch of some components etc. Can you try a different SD card (and reset settings) ? Did you buy it on-line or in a brick-and-mortar shop ? Do you have the option to bring it in for checks or have it replaced ? Did you try the other SD slot ?