What month and year did Brian crash and was rescued in Hatchet?
There is not an exact answer to this particular question. We know a couple of things from Paulsen's work which can give some level of hint to a potential answer. The first chapter of the work indicates that the time of the journey was to be "the first summer" where his father had visitation rights in wake of the divorce. We could naturally presume that this would mean that the month is June when Brian crashed into the wilderness because this would be the normal time for summer vacation in schools. For the second part of the question, the Epilogue states that Brian had been in the wild for 54 days. This would put his rescue at some point in late July or early August. There is little to indicate that the book would not have been written in the real time of publication, or around there. Paulsen himself tested out the conditions in which Brian had to endure in his own backyard, with his wife wondering what he was doing. This could be conceivable in the mid to late 1980s as the book was published in 1987.