I got your letter and I would love to answer your questions about acceleration, to help you better understand your knowledge of physics.
Well the direct definition of acceleration is the the change of velocity over a period of time.
Q1) Is acceleration just when an object is speeding up?
No. Acceleration is just the change in velocity, whether that object is speeding up or slowing down it does not matter.
Q2) When does acceleration happen?
Well as stated above it happens when and objects velocity changes. Acceleration also happens when the object changes direction. For example if a car is turning. Acceleration is a vector quanity, so that means it invloves both magnitude and direction. The speed of the car stays the same, but the direction the object is moving changes.
Q3) What is free fall and how does it relate to acceleration?
Gravity is a force and when an object is in free fall and air resitence can be neglected, the acceleration due to gravity is 9.8m/s^2
Q4) Why is acceleration a vector quantity?
Vectors include both magnitude and direction. Acceleration depends on what direction the object is traveling in(either positive and negative) and the numerical value.
I hope I have answered all of your physics questions clearly, please write me if you have any more.