Noose knot. Hangman's knot is for drop hanging. Afaik, it aids in the snapping of your neck, and the loop does not close or open as easily as the noose knot. A good noose knot, depending on the material of your rope, will slide closed (at least partially) with gravity alone. This is ideal for FSH.
As for the anchor knot, you can use a variety of different knots. Most people seem to go for the snuggle hitch, both for full and partial. I personally used a double constrictor knot, since I wanted something ultra strong (though other knots would've worked just as well). You can take a look at this megathread, if you haven't already, for some different knots to try:
hii! I haven't seen this on the website so I decided to make a compilation of all useful knots I found off of this website (animatedknots.com). I only chose knots that would be useful for hanging, I didn't consider other uses (doesn't mean it can't be used for other things). I used a shoelace...
sanctioned-suicide.net