Depends on the hemisphere.

Yes.

Yes, below the equator

Not all of them. "All low pressure systems, including hurricanes, rotate counterclockwise in the Northern Hemisphere. Here's why: When an area of low atmospheric pressure forms, wind begins to flow toward the center of it, near the surface. All the while, Earth is rotating under the atmosphere. In the Northern Hemisphere, Earth's spin causes an apparent deflection of the wind to the right, as seen from above. This Coriolis effect, as it is called, forces a counterclockwise rotation for all storms in the Northern Hemisphere. Storms south of the equator rotate clockwise." http://www.livescience.com/environment/hurricane_formation.html

Hurricanes move counterclockwise in the Northern hemisphere and clockwise in the Southern Hemisphere.

It depends on which hemisphere, the northern or southern hemisphere, for the sense of rotation. It is a result of the coriolis effect. http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html - - - - [Here is an EXCERPT from the website for you] - - - - Bad Meteorology: The water in a sink (or toilet) rotates one way as it drains in the northern hemisphere and the other way in the southern hemisphere. Called the Coriolis Effect, it is caused by the rotation of the Earth. First on this page is a discussion of the issue. Towards the bottom of the page you can see examples of incompetence from PBS,NPR, and Sports Illustrated. The Coriolis force does influence long-lasting vortices. Hurricane Andrew On the scale of hurricanes and large mid-latitude storms, the Coriolis force causes the air to rotate around a low pressure center in a cyclonic direction. Indeed, the term cyclonic not only means that the fluid (air or water) rotates in the same direction as the underlying Earth, but also that the rotation of the fluid is due to the rotation of the Earth. Thus, the air flowing around a hurricane spins counter-clockwise in the northern hemisphere, and clockwise in the southern hemisphere (as does the Earth, itself). In both hemispheres, this rotation is deemed cyclonic. If the Earth did not rotate, the air would flow directly in towards the low pressure center, but on a spinning Earth, the Coriolis force causes that air to be deviated with the result that it travels around the low pressure center. In the accompanying picture of the Caribbean, one can see the cyclonically spiraling clouds of Hurricane Andrew (at the mouth of the Mississippi) and of another vortex in the Atlantic. But, the Coriolis force is very small, indeed. water draining in the supposedly wrong way Compared to the rotations that one usually sees (tires on a travelling automobile, a compact disc playing music, or a draining sink), the rotation of the Earth is very small: only one rotation per day. The water in a sink might make a rotation in a few seconds and so have a rotation rate ten thousand times higher than that of the Earth. It should not be surprising, therefore, to learn that the Coriolis force is orders of magnitude smaller than any of the forces involved in these everyday spinning things. The Coriolis force is so small, that it plays no role in determining the direction of rotation of a draining sink anymore than it does the direction of a spinning CD. The direction of rotation of a draining sink is determined by the way it was filled, or by vortices introduced while washing. The magnitude of these rotations may be small, but they are nevertheless gargantuan by comparison to the rotation of the Earth. I decided to include a picture of a draining sink, and the first one I tried in my house was found to drain clockwise (the opposite of what the silly assertions would have it do here in the northern hemisphere). This direction was determined entirely by the way the tap filled the sink. The direction of rotation of a draining toilet is determined by the way the water just under the rim is squirted into the bowl when it is flushed. .

do hurricanes have high or low air pressure

Depends on which hemisphere. Forget which goes with which but it is the same principle as other vortex-like physical phenomena like water draining from a tub.