Is the impulse a vector quantity?
Yes, impulse is a vector quantity.
In the first equation, the average force is a vector quantity, which means that impulse must also be a vector quantity because a scalar times a vector is always a vector.
The second and third equations describe impulse in terms of momentum. Momentum is a vector since it is the product of velocity and mass, therefore impulse must be a vector quantity because the difference of two vectors is still a vector.