How can I ensure that the page height is always 100% relative to the browser? How can I prevent scrollbars from appearing on the right?

When you drop the image in, don’t crop it, and then make sure you have the “Scale Proportionally” box select when working the image.

I see that the column where image is hasn’t changed either. Which mean the image should get smaller with the column, while the text one gets wider.

Play around with setting your left column to always fit the image, thus getting smaller with it. The other one would have a min width, but expand to replace the content.

You could also, utilize padding and margin control to keep the shape of the content altogether.