We have learned the rules concerning sequence of tenses in Reported Speech. I have one question. Is the one and only possibility according English Grammar to say or to write: She told me that he loved me. Even if I am just now reproducing the sentence which was told before one hour and I want to express the fact that she loves me constantly. Is the sentence She told me that he loves me? in every occasion wrong?
"She told me that she loves me" sounds fine to me. It presumes that the love continues, but that presumption isn't wrong grammatically even if it proves to be wrong factually.
By comparison, "she told me that her middle name is Anne." In this case, it's extremely unlikely (but possible) that if her middle name was Anne before it has changed now.
And finally, "she told me that the square root of 139 is thirteen." In this case she is wrong, but the accuracy of her statement will never change.
So if it turns out she no longer loves you, her middle name is Bernice, and the square root of 169 is thirteen, expressing all of these clauses in the present tense only shows your personal expectation that the truth of what she told you would not have changed. If she just went off and married someone else, you might say "She told me she loved me," because now you have reason to believe it is no longer true, or was never true.
"She told me it was one o'clock." "She told me she was impatient." "She told me there was only a little milk left in the fridge."
All of these describe extremely changeable conditions, and you would be more likely to leave them in the past tense to indicate that they reflect a past truth. But if you know that no one has had the chance to use any milk or to buy more since she told you there was only a little left, then "She told me there is only a little milk left," expresses your expectation that this is still as accurate as it once was.