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.
A vector field is considered conservative when its curl is zero.
no
Yes, the magnetic field is a vector quantity because it has both magnitude and direction.
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.
Scaler. Its vector counterpart is the electric field.