When the ball is going upward, what happens to the force you put on the ball to send it upward?

To throw the ball upward, you temporarily push upward on it with a force greater than its weight. The result is that the ball has a net force (the sum of all forces on the ball) that is upward. The ball responds to this upward net force by accelerating upward. You continue to push upward on the ball for a while and then it leaves your hand. By that time, it's traveling upward with a considerable velocity. But once it leaves your hand, it is in free fall. Nothing but gravity is pushing on it and it's accelerating downward at 9.8 m/s². I rises for a while, but less and less quickly. Eventually it comes to a stop and then it begins to descend.

Why does the tablecloth have to be unhemmed in the tablecloth trick?

Because the hem could catch on the dishes and pull them off the table. The trick works because the slick tablecloth slides pretty easily out from under the dishes. Although it exerts some force on the dishes, that force isn't enough to make them accelerate quickly. The whole process occurs so quickly that the dishes barely have a chance to pick up any speed and they basically stay where they were. But if the hem were to catch on one of the dishes, it would exert an enormous force on that dish. The dish would accelerate enough that it would fly off the table.

How is it that the ball, when thrown upward, is acting on its own inertia when its being influenced by a force (the person throwing it up)?

I've been careless in describing the process of tossing the ball upward. There are two parts to this process: (1) the time during which you push the ball upward and it accelerates upward and (2) the time during which you are no longer touching the ball and it accelerates downward due to gravity alone. I've been trying to ignore the first part because I haven't talked about what happens when an object experiences more than one force at a time. During the first part, it's experiencing both gravity and the upward force from your hand. It does accelerate upward and this acceleration is caused by your hand. But once you let go of the ball, it continues on all by itself, driven forward by its own inertia.

I don't understand the spaceship concept (how a spaceship is falling toward the earth but missing the earth).

When the space shuttle circles the earth, it is experiencing only one force: the force of gravity. As a result, it is perpetually accelerating toward the earth's center. If it weren't moving initially, it would begin to descend faster and faster until…splat. But it is moving sideways initially at an enormous speed. While it accelerates downward, that acceleration merely deflects it sideways velocity slightly downward. Instead of heading off into space, it heads a little downward. But it never hits the earth's surface. Instead, it glides past the horizon and keeps accelerating toward the center of the earth. In short, it orbits the earth-constantly accelerating toward the earth but never getting there.

What pushes (what force) makes it (the ball) go up? You said inertia?

Here is that same problem again. The ball acquires its upward velocity from you; from your upward force. But once it is free of your hand, it continues upward all by itself. It's following its own inertia.

You said mass never changes, but doesn't it change theoretically as an object approaches the speed of light?

When objects move extremely rapidly with respect to one another, their views of the universe around them begin to change. They begin to disagree about the lengths of objects and about how quickly time is passing. Their arguments are real because the relationships between space and time do depend on their individual situations; their frames of reference. A person's views of time and space is related to that person's situation (hence the name "relativity"). If you were to pass me at a speed close to the speed of light, I would observe that your watch was running slower than mine and that your ruler was shorter than mine. Oddly enough, you would think that it was my watch that was running slow and my ruler that was shorter. Given all this disagreement about lengths and times, it's not surprising that accelerations would be something we would disagree on. Since mass and acceleration are so tightly connected, if we can't agree on acceleration, we can't agree on mass, either. I would look at you and think that your mass was extra large because you would accelerate too little when I pushed on you. From your frame of reference, I would be the one that didn't accelerate enough and that had too large a mass. We'd both push on one another with equal but oppositely directed forces and we'd both think that the other didn't accelerate quickly enough and therefore had an enlarged mass.