What is the ruling on opening an account on Twitter and publishing writings on it for all to see, and is it permissible to author a book that includes personal thoughts which have no religious or scientific benefit, taking into consideration that the writing might reveal the author’s personality and be a cause of temptation for men?

A woman is permitted to participate in social media within the bounds of Islamic law, by avoiding causes of fitnah (temptation/discord), such as joking and private conversations with men. It is better for her to limit herself to women's communities to avoid fitnah. She is allowed to write books that present her experiences and useful ideas, provided she avoids what is forbidden or provocative of fitnah, and she should purify her intention to gain reward. There is no blame upon her if a man admires her because of her intellect, as long as she remains conscious of Allah. If she fears fitnah, she should speak in a general manner that does not specifically refer to her.