The answers to your first and second have already been given in Questions 458 (website: 492) and 455 (website: 489) respectively, please refer there.
As for the answer to your third question:
Although the prophets and imams, for reasons mentioned where needed, have been chosen from amongst other men, nevertheless, this selection doesnt mean that spiritual perfection isnt possible for women and that they cant get nearer to their lord. Allah (swt) introduces women such as Lady Maryam and Asiyah (the Pharaohs wife) from previous generations as role models for mankind. Clearly, their spiritual status was and is much higher than that of many men, even of the believers. Muslims, especially the Shia believe that there have been other women whose statuses surpass that of all believers; men and women.
The mother of believers Khadijah, the spouse of the prophet (pbuh), and Lady Fatimah (as), the highest of all women, are the best examples of women whom all believers must look up to and consider as their role models.
The Shia see Lady Fatimah (as) as one who is next to the prophets and apostles of Allah (swt). Imam Sadiq (as) says that if Allah (swt) hadnt created the Commander of the Faithful, Imam Ali (as), there would be no man equal to Lady Fatimah (as). This signifies her precedence over all of the companions of the prophet (pbuh) in the eyes of the Shia.
Of course, Sunni sources are also filled with the qualities and attributes of this noble lady. For instance, they mention that she was part of the prophet (pbuh), and that bothering her is like bothering him.They also mention that she is the master/highest of all the women in paradise.
On this basis, it isnt odd that the Muslims believe that she is higher than many other men.
 Muhammad ibn Yaqub Kuleini, Kafi, vol. 1, pg. 461, hadith 10.
 Sahih Bukhari, vol. 4, pg. 210.
 Ibid, pg. 209.