Allah swt is unique in His essence.
He neither begat, nor was begotten,(112:3) nor has He any equal.’ (112:4)

Thank you for your question. It has been narrated that the 9th verse of surah 67 is revealed concerning an attempt by the polytheists of Mecca to invite the Prophet (saw) to follow the way of their forefathers after they saw the early success of his prophetic mission. They hoped that he may compromise and that they then may also compromise and reach an agreement and so they offered him money and other worldly gifts. The translation of the verse is:

"They wish that you might compromise and that they might compromise"

Thank you for your question. The answer is not known, however among the theories brought forward by our scholars is that Allah sent down houries (women from paradise) who they married.

May you always be successful

She should do qasr. 

You should perform your Salat, in your previous city that used to visit it during the week , complete. 

There is Hadith about it but with some Hadith we can't be sure that it is 100 percent true and Prophet really told that.

According to  authentic ahadith Imam Mahdi is from Ahlulbeit. It is in ahadith that he is son of Fatima (daughter of Prophet).