Question

She told me she was a student.
Можно ли сказать she said me she was a student?
Если нет, то почему?

Answer 1

Можно сказать told me, said to me или просто said:
She told me she was a student.
She said to me she was a student.
She said (that) she was a student.

Answer 2

нельзя говорить She said me. Либо
She said that she was a student или She said to me she was a student
Либо
She told me she was...

Почему? потому что правило такое, после say буз предлога можно добавлять только прямое дополнение: say hello, say goodbye, say a word