That is a very good question! You've already figured out the two things that most affect air resistance or what engineers call "drag".

The force of the air pushing past an object in motion is proportional to the object's frontal area times the square of its velocity.

To understand what frontal area is, imagine cutting a baseball in half. The flat surface that you made when you cut the ball is its frontal area or the area "seen" by the air. So you can see that velocity is the most important variable.

Let's say I throw a ball through the air. Next, let's throw a ball that is 2 times as big. We have just increased the drag by 2 times (if the drag force was 1,it is now 2). Now, let's just throw the smaller ball 2 times as fast. We have just increased the drag by 4 times (if the drag force was 1, it is now 4).

Air resistance is the number of molecules of air that an object is hitting as it travels through the air per unit of time. The faster you are going, the farther you go in a given length of time, and so the more air molecules are in your way across that distance. Likewise, if you are smaller, the fewer air molecules are in your way. So, in other words, the answer is "yes" to both your questions.

Indeed it will. The larger the moving object, the greater will be the resistance of air to its motion. This is why racing cars are very slim and low on the ground. As objects move faster, the air resistance will increase. Very often, the resistance increases as the square of the velocity, so that an object traveling at 10 m/s has a resistance that is four times larger than an object traveling at 5 m/s.

The drag force, or the resistance of a medium to the motion of objects in it, is proportional to the square of the velocity and to the Cross-sectional Area of the moving object.

Decreasing the speed will therefore decrease air resistance and decreasing the surface area will decrease air resistance. The most common method of mathematically modeling the drag force is the equation,

FD = 0.5CD*A r v².
FD = Drag Force.
CD = Drag Coefficient.
A = Cross-sectional Area perpendicular to the flow.
r = Density of the medium.
v = Velocity of the body relative to the medium.