Marine biology is a vast discipline incorporating every aspect of biology but with a marine emphasis, this ranges from ecology (which is heavily statistical) to physiology. So in answer to your question, yes it is used, the need however depends on what path you take.

Vector calculus has proved to be useful while studying marine biology.

A vector in Biology is a carrier /transporter of a virus fungi or bacteria. For example a plasmid is a vector that carries genetic information to a cell, and the mosquito is the vector of the malaria causing parasite.

A vector in biology may be an organism that transports the pathogen. Malaria is caused by a parasite which is spread through mosquito saliva. A vector for gastroenteritis is normally contaminated food or water.

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.