If you throw a dead ball at the baseball, would the baseball not roll as far as if you throw the super ball at it?

Your right. The dead ball transfers momentum only one, coming essentially to a stop on the baseball's surface. The bouncy ball transfers momentum twice by also pushing on the baseball as it rebounds. Overall the baseball receives more momentum (and also more energy) from the super ball than from the dead ball. The dead ball turns much of the collision energy into thermal energy.

How did the baseball get to be going 241 km/h when it bounced off the bat?

In the situation I discussed in class, the ball and bat were approaching one another, each moving 100 km/h in the fan's frame of reference. But in the bat's frame of reference, the ball was approaching the stationary bat at 200 km/h. The ball then bounced from the bat, rebounding with half its incoming kinetic energy. A ball traveling 141 km/h has half the kinetic energy of one traveling 200 km/h (because kinetic energy depends on speed squared). So the ball leaves the bat traveling at 141 km/h in the bat's frame of reference. Now return to the fan's frame of reference: the ball is traveling toward the outfield at 141 km/h faster than the bat. But the bat is traveling toward the outfield at 100 km/h. Thus the ball's velocity, as viewed by the fans, is 241 km/h toward the outfield.

Will our exam(s) be just like our problem sets?

No. First off, 2/3 of the exams is multiple choice questions. Second, the remaining 1/3 is very short answer questions. Those questions are ones that you basically know or can figure out in a couple of minutes, rather than having to puzzle about for a day or two.

I don't understand the rebounding idea illustrated by the swinging metal rod and the block with putty on two sides. The part I don't understand is how or why the bouncy substance transfers energy/momentum twice when the pole only hits the block once.

The bouncy substance doesn't really transfer momentum twice; it just transfers momentum for twice as long. It transfers momentum as the metal rod slows to a stop and it transfers momentum (again) as the metal rod rebounds backward. Another illustration is to consider how to knock over a massive barrel with your feet. If you run toward the barrel and hit it with your feet while coming to a stop, you will transfer all of your momentum to the barrel and it may tip over. But if you not only come to a stop, but also kick yourself backward, you transfer even more momentum to the barrel and are even more likely to tip it over.

In high school, we said that an object on the ground had zero gravitational energy, while an object above the ground has some. But if a hole opened up in the floor, the object on the ground would fall - so it must have SOME potential energy, right? At the center of the earth, would you have no gravitational potential energy? If not, why - doesn't the sun still pull on you?

You've brought up an interesting subject. Many quantities in physics are only well-defined relative to some reference point. For example, your velocity is only defined relative to some reference frame; typically the earth's rest frame. Viewed from a different reference frame, your velocity will be different. The same holds for gravitational potential energy. When you choose to define the object's gravitational potential energy on the floor as zero, you are setting the scale with which to work. For altitudes above the floor, the object's gravitational potential energy is positive, but for altitudes below the floor, that energy is negative. As the ball falls into the hole, its gravitational energy becomes more and more negative and its kinetic energy increases. To avoid working with these annoying negative potential energies, you should choose to set the gravitational potential energy to zero at the lowest point you'll ever have to deal with; for example, the center of the earth. But the center of the earth isn't really the limit of gravitational potential energy. The object could release even more gravitational potential energy by falling into the center of the sun. It could release still more by falling into the center of a giant star. Fortunately, there is a genuine limit. If you were to lower the object slowly into a black hole, the object would release absolutely all of its gravitational potential energy. In fact, it would release energy equal to its mass times the speed of light squared (the famous E=mc2 equation of Einstein). The object would actually cease to exist, having been converted entirely into energy (the work done on you as you lower the object, presumably at the end of a very sturdy rope). This effect sets a real value of zero for the gravitational potential energy of an object: the point at which the object ceases to exist altogether. Final note: if you drop something into a black hole, it doesn't vanish the same way, because its gravitational potential energy becomes kinetic energy as it enters the black hole. The black hole retains that energy and grows slightly larger as a result. When you low the object on a rope, you retain its energy and it doesn't remain with the black hole. The black hole doesn't change as it "consumes" the object.