Calculus can be used for many applications for marine purposes.
It can be used for calculations of wear, temperature (e.g. using newton's law of cooling ect) or even calculation for control systems or stability of control systems ect.
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Generally pre-calculus is taken after trigonometry, unless the trigonometry course was supplemented by a pre-calculus course, in which case the next course would be calculus.
Calculus is commonly taken as a first year course in college, but can be taken as an advanced course late in high school through programs like AP Calculus.
Simply put, calculus is an intermediate branch of mathematics that deals principally with variables.
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.
In many universities and colleges this is a course covering various topics in physics that avoids using the calculus.