The issue here is 'collocation': some words are often used together and some words are almost never used together. For example, English speakers often say "best friend", but do not often say "favourite friend".
"[M]utual help" is a collocation; these words are often used together. "[R]eciprocal help" is not a common collocation. The words are not interchangeable in your sentence, though everyone would understand the meaning.
"Reciprocal" and "trade" are often used together. At least in the UK, "mutual" has a special legal meaning when it is used with "trade" (perhaps similar to 相互 in Japanese 相互会社). So I think business experts would try not to use "mutual" interchangeably with "reciprocal". In less formal writing and speaking, "mutual" might be acceptable in this sentence.
And I think that mutual is almost always written before a noun, except in a fixed expression ("the feeling is mutual"). This is not mentioned in the Oxford Advanced Learners Dictionary though, so I may be wrong on this point.
I hope that helps!