Yep, that's fine. Finder isn't colour-managed, you see. It's perfectly normal (though annoying, I agree.)
All that matters is that Photoshop matches your pro lab prints. Does it?
Great!
So just do exactly what it says. Choose your Crop Tool, enter 40 and 50mm in the Width and Height fields, and 200 in the Resolution field, and crop, then sharpen. That's all there is to it.
Make sure, when viewing it after the crop, you don't zoom further in than 100%. It sounds like you must have been doing so.
I did some searching on other sites, and yes, it doesn't look like that ASUS has an IPS screen.
Pity, because the IPS screens in ASUS laptops which do have them are amazing. I love mine. It calibrates so beautifully.
Please try not to edit on externals. That's fraught with risk. Externals are only for backup and long-term storage.
Were you cropping when these ones had their problems too? Or were you doing something else?