1) Is it permissible or not for women to write and publish beneficial books on religious and other permissible subjects and topics which include fiction (poems, stories) and non-fiction (research, education, biography, etc.)? Is the writing of women considered ‘Awrah (what should be covered of the body)? If her writing (books) are read by non-Mahram (permanently unmarriageable) men, is it a sin or not?
2) Can she keep a personal diary?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

It is permissible for the Muslim woman to write and publish books in any useful field of knowledge as well as to write her diary if it does not include inappropriate content. She is just like the man in this regard.

In principle, women are included in the religious rulings that address men, unless the textual evidence clearly specifies that it addresses men only or women only. Allah, The Exalted, says (what means): {Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life, and We will surely give them their reward (in the Hereafter) according to the best of what they used to do.} [Quran 16:97]

Moreover, the Prophet, sallallahu ‘alayhi wa sallam, said, “Women are the counterparts of men.” [Ahmad and others] Al-Khattaabi wrote, “It is deduced from this hadeeth that Qiyaas (analogy) is valid ... and that the addressed audience of the religious texts includes both men and women even if the wording indicates that it is addressed to men, except in the places that address women specifically.” [Ma‘aalim As-Sunan]

The woman's writing of books and the like has nothing to do with the ‘Awrah. It cannot be said that the writings of the woman are ‘Awrah; rather, it is allowed for the Muslim woman to teach knowledge, and there is no harm if men listen to her voice provided that she refrains from softening her voice (speaking in an alluring, tempting, soft manner) and the like. The most likely correct view in this regard is that the woman's voice is not ‘Awrah.

Lastly, we would like to draw your attention to the religious conditions and guidelines regarding writing fictional stories and the like; please refer to fatwa 83691.

Allah knows best.