p.32 question 3 asks us to "suppose f is a translation through a fixed vextor, what is the composition of f followed by f?" - is it simply asking us for the notation which would = f(2v) ?
No. It is not asking for notation and the notation that you give above is not precise (for f(2v) would read "f applied to 2v", which is not a correct answer). It is clear from what you wrote above that you know the answer of that question. Perhaps the simplest way to express it would be by using words. For example, "translation through the vector that is 2 times the given fixed vector" is a good answer. With the established notation, one can write "trans(2v), where v is the given fixed vector". Both answers are O.K.