And don't you dare get me started on what his son has done with Frank Herbert's notes.
To answer your questions:
1. At first, many of the colonists tried to keep women in their traditional roles. But as with women who migrated to the US western frontier, there were too many jobs and too few hands to keep those roles in place. In the time of my stories, around 2320, the status and power of women has become much elevated, even honored, among Martian Muslims, which has led to strident religious arguments with conservative Muslims that did not emigrate, who who emigrated latter.
2. As with the status of women, the status of education was forced to radically change, for one simple reason: there are no
suras instructing the faithful on how to build and maintain atmospheric scrubbers, water recyclers and hydroponics facilities. Survival required a strong education in highly technical fields, which helped to spark the renaissance of Muslim science I mentioned above.
3. The Sultan of Oman and his immediate successor put most of the Sultanate's considerable fortune towards this enterprise. Many Muslim groups helped as well, some out of a sense of brotherhood and some (sadly) out of a sense of "good riddance." Religious scholars held that the obligation of the
zakat could be met by giving money to any of the groups promoting Martian emigration. Also, the Departure of the Exiles saw a brief revival of bonded servitute, where individuals and even whole families sold themselves into service for a period of time (typically between 5 and 10 years) in exchange for passage and a place in the Martian settlements. Technically illegal by national, international and religious law, the practice continued for almost a century.
4. When the Departure began, there were three permanent settlements on Mars, all scientific research outposts. Al-Merrikh (the Arabic name for Mars) was owned by a conglomerate of investors, with the Sultanate of Oman as the chief stockholder; it was here that the first wave of emigrants arrived.
When the Republic of Al-Merrikh was proclaimed, there were 28 fully established settlements, and four others in various stages of construction. Most of these had been built by Muslims and were, as you would expect, populated almost exclusively by exiles. Of the two that did not vote for union, one was controlled by a group who felt that Martian Islam was not "pure" enough and wished to remain separate; the other was one of the original research outposts that wanted to remain apolitical. All of the settlements had significant minorities of non-Muslims; again, the rigors of colonial life on a harsh planet forced most of the purists to modify their attitudes and to accept "infidels" among them.
In the two and a half centuries since, the number of (known) settlements has expanded to 102. All of these are subject to Al-Merrikh law which retains elements of
Sharia. Some of these settlements, however, are designated as "secular" and thus exempt from many aspects of religious law. While largely populated by non-Muslims, more and more Islamic Martians have been moving to them, seeking to escape rules they see as outdated. Several settlements have also begun agitating for secular status, and the threat of another religious war is visible on the horizon.