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.
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.
Yes, it is.
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
Vector.
no
Scaler. The electric field is its vector counterpart.
Direction of the electric field vector is the direction of the force experienced by a charged particle in an external electric field.
in which field vector calculus is applied deeply
Charge is not a vector.
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.
Yes, every irrotational vector field is conservative because a vector field being irrotational implies that its curl is zero, which, by one of the fundamental theorems of vector calculus, implies that the vector field is conservative.
No, the velocity vector of a charged particle is not affected by the electric field if it is perpendicular to the field. The electric force acting on the particle is zero in this case because the force is given by the product of charge and the component of electric field parallel to the velocity vector.
Scaler. Its vector counterpart is the electric field.
Yes, the gravitational field is a vector quantity. It has both magnitude (strength) and direction, which are important in determining the effect of gravity on objects within the field.