Can velocity be zero if accelerating?
For the most part velocity is not zero if an object is accelerating. Since acceleration is the change in velocity over time, there has to be a change in velocity for something to accelerate. In other words, if something is accelerating, it has to have a variable velocity. If the velocity is constant however, the acceleration is zero (because the velocity isn't changing over time).
Although at an instant in time it is possible to have zero velocity whilst accelerating. For example, if you drop an object at the instant you release it it has zero velocity but it is accelerating. Also if you throw an object upwards it will by subject to an acceleration throughout its flight time, however at the very top of its trajectory it will have zero velocity for an instant in time.
This is the reason that in simple harmonic motion you will notice that when the oscillating object is at maximum displacement it has zero velocity but is experiencing maximum acceleration. To see the graphs see this tweet: https://twitter.com/lscphysics/status/386625575013466112/photo/1