I did find an article that states what your answer is:
READ IT HERE
And here is another one that states your teachers 'right' answer is actually an urban legend.
First off, we need to be clear on something: this idea that water drains in a bathtub (or sink or toilet or whatever) one way in the northern hemisphere and the other way in the southern hemisphere isn't true! It's what's called an urban myth, or modern legend; an idea that gets propagated and never seems to die, even though it's wrong!
The coriolis effect is what makes this legend so tenacious. Picture the rotating Earth: at the Equator, you travel about 40,000 kilometers in a single day as the Earth turns. At the poles, you simply spin in place with no movement at all. If you shoot a projectile from the Equator towards the pole, the projectile will try to keep that sideways motion, and so it actually moves sideways faster than the ground beneath it as it moves toward the pole. Whether you shoot the projectile north or south, the projectile tends to move east as it heads toward the pole, outracing the ground underneath it.
This effect is what causes hurricanes to spin, and why they spin in opposite senses in the two hemispheres. Pretend you are on the equator facing north. Wind moving north (away from you) tends to turn east (right), while wind heading south (towards you) tends to head west (left). This gives the hurricane a counterclockwise spin. Now face south, towards the southern hemisphere. Wind moving south (away from you) tends to head east (left), while wind heading north (towards you) tends to head west (right). This makes the hurricane spin clockwise.
Note (1/10/99): I originally said northern hemisphere hurricanes move clockwise; that has been corrected here.
But this only works over distances where the spin of the Earth makes a difference when you head north or south. Your bathtub is simply not big enough to make a difference. Random currents in the water completely overwhelm any tiny coriolis effect going on. Imperfections in the drain also have a larger effect.
Now, if you could somehow completely dampen the random currents, you might be able to see the effect. So, assuming you can, and the drain is a perfect circle, the answer to your first question is that on the equator, it should simply drain straight out, with water coming in from all sides equally.
On a space station with no gravity*, the water won't drain at all! After all, it's gravity that pulls the water out of the basin in the first place. However, imagine you are on a rotating space station, like the one in "2001: A Space Odyssey". The coriolis effects can be very large, because the station spins once every minute or so! As you head "down", away from the central axis, the station is moving faster-- this is analogous to moving towards the equator on Earth. If you were in a tube and let yourself fall from the center, you would feel yourself pushed against the tube as you moved down, in a direction opposite the spin direction. If you dropped a rock from the station axis (which would no doubt get you a free ticket back to Earth from an angry commander!) it would appear to arc strongly in the anti-spin direction as it fell, and the station rotated underneath it. Anybody building a plumbing system on a space station would have to keep that in mind!
*Oops! (August 7, 2002): there is gravity in orbit! Gravity goes on forever, and in fact the Earth's gravity in low Earth orbit is about 90% what it is on the surface. What I meant here is that in orbit, the astronauts on board the space station feel as if there is no gravity because they are in free-fall. I didn't mean to propagate Bad Science here!
I have a list of urban legends that involve astronomy,
including a link to an excellent page about this particular myth.
I suggest you print out the sources I gave you and present them to your teacher. I hope it helps your grade go higher.