Student or Learner
When we report an intention, hope or promise, we use an appropriate reporting verb followed by a that-clause or a to-infinitive:
"I'll pay you the money tomorrow."
He promised to pay me the money the next day.
He promised that he would pay me the money the next day.
When we want to report an order or request, we can use a verb like 'tell' with a to-clause.
"Could you please be quiet," she said.
She asked me to be quiet.
My question is do we have to use this rule or can we report them like that?
"I'll pay you the money tomorrow," she said.
He said she will/would pay me the money the next day instead of he promised to pay me the money the next day.
We can report speech as we wish, provide the results are grammatical. Yours are fine = so long as you change 'he' to 'she'