All sentences are mine:
(1) If it rains tomorrow, he will not go to the beach.
If "tomorrow" remains after backshift, it means tomorrow has not yet come, so backshift is optional. That is:
we may backshift (1):
(2) He said that if it rained tomorrow, he would not go to the beach. – correct
we may not backshift (1):
(3) He said that if it rains tomorrow, he will not go to the beach. – correct
but we can't backshift only one clause as in the following two sentences:
(4) He said that if it rained tomorrow, he will not go to the beach. – incorrect
(5) He said that if it rains tomorrow, he would not go to the beach. – incorrect
"The next day" shows us that tomorrow already passed, so we must simultaneously backshift both "rains" and "will". That is, of the following four sentences, only (9) is correct:
(6) He said that if it rains the next day, he will not go to the beach. – incorrect
(7) He said that if it rains the next day, he would not go to the beach. – incorrect
(8) He said that if it rained the next day, he will not go to the beach. – incorrect
(9) He said that if it rained the next day, he would not go to the beach. – correct
Tell me please where I'm right and where I'm wrong and why?