I can answer part of your question, I think.
Invisible (AKA provisional) cast-on is used when you are going to need to free up the stitches of the cast-on row. I know it from the Moebius scarf pattern. You can free up the cast-on row back easily to weave, or put them on a needle and knit in the opposite direction from the original body.
I know how to make a half-hitch on a rope, but I've never heard the term used in knitting. I'll be watching this thread to find out.