Yes, by all means give it a shot. But it's a heck of a fiddly and frustrating process, so brace yourself.
It certainly shouldn't need to happen. But in desperation, yes, you can try it.
Oh, any pastel-ish wall colour is fine. As long as it's nothing garish that throws cast around.
I know it's a hassle for a desktop computer, but have you tried setting it up in any other rooms, that might be better lit, to see what you see?
Your prints aren't too dark. Your prints are what they are. The job of monitor calibration is to make the screen match the prints.
No chance at all, I promise.
Then it's time for a new screen. Let's not waste any more time on this.
However, when I say "new" I don't actually mean new. https://www.facebook.com/groups/195567190503489/permalink/2659777307415786/
It really sounds like graphics card interference in your new computer, doesn't it? I can't think of any other explanation.
Maybe see if it's possible to temporarily turn off the graphics card?