In which case, can velocity be negative? displacement be negative?

An object which moves in the negative direction has a negative velocity.

Yes. Displacement is a vector, as opposed to distance, which is a scalar. Since displacement is a vector quantity, the negative sign represents direction.

As with velocity and acceleration, it just comes down to how you define your coordinate system. In a 1D example, if you set yourself as the origin, objects to your right could be "positively" displaced while objects to your left are "negatively" displaced. Distance, on the other hand, is always positive.