Spacing notes and Editing measures

It seems you've modified several style settings from their default, and in ways that don't think are helping, except that they are allowing you to fit nine measures of a relatively large staff onto relatively small paper. I'd personally have simply turned down the staff size a bit if I needed it to print on such small paper.

But I'm still not really understanding what you mean about evenly arranged notes. The picture from the printed book shows the same sort of unevenness I absolutely expect. For instance, the width of measure one is clearly less than that in measures 4 or 6, resulting in tighter spacing.

In the second example, I am looking at measure 18. It's wider than 12 above because it's on a different system where the other measures are different. if you artificially make 18 narrower, everything else on that system will become too wide to make up the difference (to keep the system stretched all the way to the right). The current spacing is correct - there are fewer measures on the system, fewer notes, no time signature changes, so of course everything is spaced more widely. If you want the spacing between the systems to be more even, try adding a system break to measure 11. now the systems are better balanced.

"Stretch" is the MuseScore term for how we adjust measures widths. For each measure, we calculate the minimum width necessary to fit everything in given your style settings. We then multiply it by whatever the "stretch" value is. You can set it directly in that dialog, or use the commands in Format / Layout Stretch. After multiplying, this tells us the measure will be at least that large, but then everything is stretched more as needed to fill each system to the right margin.

So if you have two measures on the same system with the same notes, they would normally be the same width. if you increase stretch for one, or decrease it for the other, then the first will end up wider than the second. If you change stretch for both by the same amount, then they will remain the width. It's all relative.

So in your example, you can certainly increase stretch on measures 13-17 to force 18 to be smaller in comparison. The results are definitely worse though. Now 13-17 are way too wide, and 17 looks comically narrow in comparison.

The defaults should normally be left alone unless you are an expert music engraver who really understands these issues and the specific times when the defaults do actually need to be fiddled with to produce better results.