A vector is represented graphically as an arrow. The direction indicates the direction, the length is proportional to the magnitude of the vector. Note that it is difficult to accurately represent vectors of 3 or more dimensions on a 2-dimensional sheet of paper.
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Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
Lenght
Velocity.
Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.
The length of the arrow signifies the magnitude or size of the vector.