The number of batteries sold per week by a garage may be assumed to have a poisson distribution with mean 5.

a) Find the probability that

i)exactly 6 are sold in a randomly chosen week

ii) exactly 6 are sold in each of 3 randomly chosen weeks

iii) exactly 18 are sold in a randomly chosen 3-week period.

b) Find, approximately, the probability that more than 240 are sold in a randomly chosen 52-week period.

OK firstly i write

X~Po(5)

for a-i i get this

is this agreed?

for part a-ii i'm not sure whether to simply do

Right
or rewrite X~Po(15) ...?

No, then you would be ignoring the "in each of 3 weeks" part of the problem and just looking at the total number.
part a-iii presents the same problem.

for part b i try

X~Po(5*52) = X~Po(260)

but i'm not sure :/

The approach is right but your arithmetic is wrong.