The page size (outline) and the data frame (which are visible in your images) are two different things, and are not automatically adjusted to each other. You have to do that manually when changing layout/page size (this is why I always use layout templates). ArcMap doesn't know how much of your page each (if you have more than one) data frame should cover, where you want space for legend etc.
So there are two issues with your layout: 1) the dataframe does not cover your whole page (which it doesn't have to, but it seems like you want that), 2) the dataframe is not placed entirely inside your page, which causes the behaviour seen in the second image.
Solution: Add a few guides to your page layout, say 5-10 mm from the page outline, and snap your data frame to them. That'll give you a full page map to work with.
EDIT: I now see that you use the Print dialogue for creating PDF files. If you instead use the Export option (File --> Export map...) you have more control over resolution, colorspace, if you want to export with vector layers etc.