For example, I have books of stitches for granny squares. Can I
demonstrate these stitches with the video? Or would that violate the
author's copyright? Also, if I find free patterns, such as from Lion
Brand Yarn, can I demonstrate these on the video?

Any stitch that is concidered as a "public domain", let's say
chainstitch, you can use. All the stitch library books etc. if you can
find the same stitch in several books from different authors, you can
use. No one can copyright basics. If you don't show the actual book, nor
the instructions from the book, it's ok. You make your own piece and you
have a copyright to those works.

Johanna