If force causes only acceleration and not velocity, does a machine (i.e. an engine) that causes a constant velocity in an adjacent object not exert a force?

If that adjacent object is free of any other forces, then no, the machine does not exert a force on it! This is a wonderful question, because it points toward many of the issues concerning energy and work (topics we will discuss in a few days). The bottom line is this: if some object is truly free-moving (no other forces on it), it will move along at constant velocity without anything having to push on it. For example: if your car were truly free-moving (no friction or air resistance), then it would coast forever on a level surface and the engine wouldn't have to do anything. You could even put the car in neutral and turn off the engine. The only reason that you need an engine to keep pushing the car forward is because friction and air resistance push the car backwards.

Why does acceleration change when an object changes direction?

What you mean by "changes direction" is that the direction part of its velocity changes. For example, instead of heading east at 10 m/s (or 10 miles-per-hour, if that feels more comfortable), it heads north at 10 m/s (or 10 miles-per-hour). This change in direction involves acceleration. The car must accelerate toward the west in order to stop heading east, and it must accelerate toward the north in order to begin moving north. Actually, it probably does both at once, accelerating toward the northwest and shifting its direction of motion from eastward to northward. The question as you've asked it doesn't really make sense. What you probably wanted to ask was "Why does velocity change when an object changes direction?"

I don't understand the relationship between mass, acceleration, and force in Newton's second law.

First off, force causes acceleration. The strong that force, the more the acceleration. In fact, the two are exactly proportional to one another: double the force and you double the acceleration. Secondly, mass resists acceleration. The more mass an object has, the less it accelerates. The two are exactly inversely proportional to one another: double the mass and you halve the acceleration. These two ideas can be combined into one observation: the force you exert on an object is equal to the product of its mass times the acceleration it experiences. Look at that relationship: if you double the force you exert on an object, you double its acceleration, so that part checks out. If you double the object's mass and leave the force unchanged, then the acceleration must be halved, so that part checks out. Thus Newton's second law is simply a sensible relationship between the force you exert on an object and its mass and its acceleration.

Is acceleration also a decrease in speed?

What you mean here is "are you accelerating when your speed decreases?" The answer is yes! If you are walking east and you come to a stop, it is because you accelerated to the west! By "deceleration" is acceleration in the direction opposite our direction of motion. Thus in a car, when you stomp on the brake and decelerate, you are actually accelerating toward the rear of the car (in the direction opposite its direction of motion).

I learned that acceleration is not a measure of just speed, but also of direction.

Actually, the appropriate word here is "velocity," not "acceleration." Velocity consists of speed and direction of travel. Acceleration, while also a directed physical quantity (also called a "vector quantity"), doesn't involve speed. Instead, it's related to changes in speed (and also direction of travel). This distinction is important but difficult to grasp and requires thought and perseverance.

Why is force=mass*acceleration an exact relationship (i.e. why not force=2*mass*acceleration)?

The answer to this puzzle lies in the very definition of force. How would you measure the amount of a force? Well, you would push on something with a known mass and see how much it accelerates! Thus this relationship (Newton's second law) actually establishes the scale for measuring forces. If your second relationship were chosen as the standard, then all the forces would simply be redefined up by a factor of two! This redefinition wouldn't harm anything but then Newton's second law would have a clunky numerical constant in it. Naturally, the 2 is omitted in the official law.

Why do you feel no acceleration in free fall, even though you are accelerating.

This wonderful question has many answers. The first, and most direct, is that you do feel the acceleration. You feel an upward fictitious force (something we will encounter in a few weeks) that exactly balances your downward weight. The feeling you experiences is "weightlessness". That's why your stomach feels so funny. You're used to having it pulled downward by gravity but the effect of your fall is to make it feel weightless.