Velocity is change of position, so if the velocity is zero that means the position must not be changing. If you lift you hand straight up then straight down again there is a point at the top where the position isn't changing. We know this because as you move your hand up the height is increasing and as you move your hand down the height is decreasing. There must be a point in between where the height is neither increasing nor deceasing i.e. at this point your hand is stationary and the velocity is zero.
However if you move your hand straight up then sideways you can't use this argument. At the moment the height stops increasing a sideways movement starts. There is not a point where neither the height nor the sideways position is changing, so the velocity is never zero.
Acceleration is a bit simpler because acceleration is the change of velocity. Velocity is a vector and change in direction is also a change of velocity, so if your hands or feet change direction there is always a non-zero aceleration.