(a) Is it possible to be accelerating if you are travelling at constant speed?
(b) Is it possible to move on a curved path with zero acceleration, constant acceleration, variable acceleration

Explanation

If speed is constant, velocity may change due of velocity so acceleration may not be zero when speed is constant. Actually in uniform circular motion speed = constt but acc. `!=0`.
For motion on a curve we at lest have to change the direction of motion, so we will require a force, and hence acceleration, i.e, it is not possible to round a curve with zero acceleration. However, in rounding a curve acceleration may be constant or variable. In case of projectile motion acceleration is constant `(=vec(g))` while in case of circular motion acceleration `!=` const. either due to change in direction or both change in direction and magitude.