It is the rate of change in the vector for a unit change in the direction under consideration. It may be calculated as the derivative of the vector in the relevant direction.
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Vector.
Direction of the electric field vector is the direction of the force experienced by a charged particle in an external electric field.
Charge is not a vector.
Gradient= change in field value divided by the distance
When one refers to the strength of a magnetic field, they're usually referring to the scalar magnitude of the magnetic field vector, so no.