Is the hadith true which mentions that a woman who cuts her hair very short will be dragged by angels from her breasts in the grave for questioning, and that if she had not cut it, she would have been dragged by her braids?

We have not come across a Hadith with this meaning regarding matters of the grave. As for a woman shortening her hair, it is permissible by the length of a fingertip (an anmulah) during Umrah and Hajj. It is also permissible out of necessity, such as to lighten the hair or for treatment. However, it is disliked to shave or cut hair without a valid excuse, and it is forbidden if it is intended to imitate men or disbelieving women.