I open Inkscape, go to page setup, set it to A4 and enable a grid of 1cm blocks.

Then I click on the snapping bar and enable snapping.

Then I click the rectangle tool, to try to draw a rectangle. Then it draws this:

WHAT!!? I can't show you because I can only embed a Youtube Video?!!? (Is this for real or did my brain get damaged somewhere without my knowledge?)

I uploaded it to Imgur: https://imgur.com/5RfWG3O.png

It draws an ellipse. I don't get it. I have clicked around, looked that the fill, stroke, I can't find anything to do with corners.

Please help me. All I want to do is make a centimeter scale for photographing small objects.

Thanks
 

I think you've rounded the corners of your rectangle. There's a button on the toolbar that will return the corners to sharp. With the rectangle tool selected, click your object then look for the button shown in the screenshot below. Hopefully that should fix things.