Shift Key when dragging shape doesn't make them perfect circle or square

Eh, it happens. Don't beat yourself up over it. There's so much to learn about video settings, formats, codecs, etc. that it can take a long time to understand everything. My best advice is when something doesn't work the way you think it should (especially in After Effects), don't assume something is broken. There's probably a very good and technical reason for it. Obviously, that's not to say that there aren't bugs, so always feel free to ask questions and file bug reports and feature requests at the User Voice site, but keep questioning why things are the way they are, rather than just accepting them.

What is the Pixel Aspect Ratio of your comp? You can find this by going to Composition > Composition Settings or hitting Cmd/Ctrl+K. In most cases you're going to want to work with Square Pixels (see attached screenshot). I'm guessing your setting is one of the other options.