Gimp: Increasing resolution doesn't shrink image?

Question

I'm so done with this topic ... resolution, pixels, inches, ppi, dpi and all that stuff. I never find a source of explanation which puts me in a state of not-wondering-anymore. Once I have reached that state I'll write a blog post myself.

So, first question: I have an image which I open in Gimp. I click on "Image -> Scale Image". It says my image has 826x1169 pixels at a ppi of 100. Thus the width of my image must be 8,26 inches. I held a goddamn ruler against my screen (feeling stupid doing this): width is 6,1 inches. Why not 8,26? The image demands that its 826 pixels are displayed at a ppi of 100. Why does my screen say "Nope, I only have 6,1 inches for you today, buddy. So I'll squeeze your 826 pixels into those 6,1 inches, enjoy your ~135 ppi lol bye."

Second question, same image: Again I click on "Image -> Scale Image". The "X resolution" and "Y resolution" are chained together. I take it down from 100 to 50/20/whatever. I click on "scale", feeling very confident that my image will shrink since I demand the machine to use more of my precious 826 pixels for each inch ... aaand: nothing changes.

Can someone enlighten me? I got a feeling that both questions are related somehow.