Egg in a hole (Kentucky). We use egg in a basket or egg in a nest if it's hash browns instead of bread.

Technically, no spinning from the Coriolis effect. Realistically, something tiny like you reaching into the water will create enough movement that you'll get it going one way or another.

For something like a toilet where water is staying into it, the force of the spray itself is all that really matters. But, for water that is still (pulling the drain on a bathtub), then yes, absolutely this is true. The spin will be the same as a hurricane (depends in hemisphere), and for the same reason.

For ELI5, think of it this way. The earth is spinning, and at the equator it's moving really fast, like 900 mph. At the north pole, the earth isn't moving at all, so in the northern hemisphere, you can picture all land to the north of you as moving slower than you, and land to the south as moving faster than you. If you run south, it would spin you because it's moving 'sideways' faster than you are. Cross the equator and suddenly it gets slower as you run south, literally putting the brakes on your spin.