Only use sensor cleaning swabs and solution made for the job. They are expensive but a lot cheaper than a new sensor. You may have to do it twice or more but my guess is that it will work.
Switch the shutter to ES to prevent any possibility of the mechanical shutter going off while cleaning.
Turn on the camera and leave it on
Set IS mode to off.
Clean.
Your camera has three different auto white balance settings, you may be using one that is not suitable for the lighting you have to deal with.
Some of the reviews mention this, I have listed two for you to read, the fstoppers one uses an old approach to deal with this: a quick custom white balance, essentially it is the old ‘put a bright white coffee filter over the lens, use the menu to set a custom shite balance with a single shot and use that as white balance until the lighting changes’ trick but you can read their version in the article, or try the other auto white balance settings.
https://www.photoreview.com.au/reviews/medium_format/fujifilm-gfx-100-ii/
https://fstoppers.com/education/tips-shooting-fujifilm-gfx-100-405452
The blurry screen image … do you have another camera to get an image so that you can compare that to the image in the file?
p.s. Welcome to the forum.
Hi. I'm from Spain. I jumped from film to digital with a Fuji S3 Pro many years ago (I still have it), then I've been using several Nikon bodies and way more lenses than I need 🤷♂️. I wanted a smaller, lighter and sexy body for traveling and casual use so I ended up with a XT30 II, a 35mm f2, a 16mm f2.8, a Godox TT350F and a X2T trigger.
Now I'm extremely happy with my very small, very light and very powerful bag.