No - the direction the toilet water spins depends on the small scale vortices created when you flush. The Coriolis effect is slow - it acts at a much longer time scale.

In theory, yes. However other factors such as the shape of the drain, the shape of the toilet bowl, and any small initial motion in the water, usually completely overwhelm the coriolis effect. You would only be able to observe it under extremely carefully controlled conditions: extremely still water, and a completely symmetrical toilet bowl perfected to extreme, micron precision.

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.