Here is a summery of my impressions.
Four Sided Stitch
It is easy and rhythmical. Each square could be used to frame crosses, knots, beads or sequins. Apart from that it is obviously great for filling empty spaces.

A descriptive name for this stitch which indeed looks like a gate. It makes a compact filling stitch but also gives you a proper gate in a fence.

Heavy Chain Stitch
Oh, this fun and easy to work stitch leaves a rich cordlike line and can be a good replacement when you want something more dominant than a stem stitch. It 'writes' well and is perfect for monogramming or handwriting.

Interlaced Running Stitch
My box of fancy threads asked to be opened and out came cries of 'Use ME' and 'I want to LACE those Running stitches'. It was so much fun playing around with them all. There is no end to how this stitch can be spaced, curved and laced.

Japanese Darning Stitch
Worked row upon row it makes a neat filling stitch, while in two rows it forms a unique ornamental border. As far as I can see it has no connection to Japanese embroidery.

Revision Homework:
Use the five stitches on this modern design of Sunbonnet Sue.