Velocity increase while acceleration decrease? I'm having trouble understanding velocity and acceleration.

Is it possible for velocity to be increasing while acceleration decreases and vice versa?
Sure, as long as acceleration is positive, velocity increases, even if acceleration is decreasing (as long as it doesn't reach zero).

Likewise, as long as acceleration is negative, velocity decreases even if acceleration is increasing.
As long as a is not zero v is increasing because the body has certain instantaneous a. But if a is increasing v does not decrease. If the body has decalaration only then v decreases.