For the second part, countries such as Lebanon, Syria, Mandatory Palestine and Israel, etc.
Thanks!
While I cannot go much deeper into the areas beyond the 'era of modernisation', I believe I will be able to delineate a general picture. The turning point, it seems to me, lies in this era from the 19th century onwards. But I cannot help much about the impact of the Ottoman family law(s) to the Ottoman successor states mainly because I focus on Turkey and, as we will see, Turkey abolished even the 'secularised' version of the Ottoman family law in the Republican era.
The social and legal ordering of the Ottoman society before and after the era of Tanzimat (beginning in the 1830s and really kicking off in 1839) followed the lineages of the 'millet system'. According to this, all major non-Muslim groups were treated as separate, quasi-independent 'states within the state'. The very word millet is ambiguous here; it used to refer to this ethnic-religious groupings before and has come to refer more strictly to the ethnic-national groups today. Each 'millet', Jews, Greeks or Armenians, had their own religious laws, presided over by their own clergymen, applying their own religious rules. As for inter-confessional issues in family law, no such a thing existed to my knowledge, barring one example. According to Islamic law in the Ottoman Empire, a Muslim woman could not marry a non-Muslim man. A Muslim man could marry a non-Muslim woman but, on the condition that the offspring will be raised as proper Muslims. To ensure this, sometimes the woman was asked to convert to Islam before the children grew sufficiently to understand and be influenced by their mother on such serious issues.
The Islamic law itself is I suppose better known. It allowed for, but in the Ottoman case tended to discourage, polygyny. A man was allowed to marry up to four women. He was also supposed to take care of them and to treat them well by providing for them. Though it would wane in comparison with what women in most countries have nowadays, women had a legal right to make complaints about their husbands when they violated any part of their marriage contract and had the right to divorce. Roughly speaking, this was the Islamic law as practised under the Ottomans.
Family law remained the untouchable area of law in the Ottoman Empire under the Tanzimat era. What I have depicted above, in fact, used to apply to a variety of other legal fields. The new 'Nizamiye Courts' that appeared first to address commercial cases during the Tanzimat began to encompass wider areas of Ottoman society with time. This they did generally by applying laws that were either modelled after Western (generally French) laws or partially translated from them. However, scholars such as Avi Rubin remind us that this should not be read as a triumphant march from the Islamic era to the radically Westernising era. The personnel of the Nizamiye courts happened to be the same chaps that participated in dealing with the Sharia cases, for instance. Rubin also downplays the role of direct Western inspiration in legislation. I would not go as far to say there are multiple modernities (if modernity and the diffusion of Western practices will have any meaning for our historical analyses) but he is absolutely right that the Tanzimat era was not one giant step towards the inevitable goal of radical Westernisation in law and society, as it were. As before, more importantly, the family law remained the field of the Shariah (and other religious courts). Towards the end of the Tanzimat, Mecelle emerged as a codified, formalised version of Islamic law. It was rumoured that one of the Tanzimat statesmen, Mehmed Emin Ali Pasha, actually wanted to import the French Civil Code but was admonished by the more conservative elites not to go too far. We do not know whether this is true or not but what is certain is that even the Tanzimat did not bring about a major change in the issue of family law. Importantly, even Mecelle itself did not touch upon the subject of family law much, presumably because Mecelle was intended for use in the Nizamiye courts and the family law was still seen strictly as the business of religious courts.
The most important change in the imperial era occurred during the First World War, when the Committee of Union and Progress passed a decree called 'The Decree on Family Law' in 1917. The decree is sometimes seen as the hallmark of the new, secularised, 'modern' Ottoman family law. This is certainly an exaggeration. The law codified and formalised Ottoman Muslim family laws by drawing on a variety of Muslim schools of thought. It regulated the application of family law (much as previous steps tried for different areas) predictable and formal. In the past, a certain degree of legal pluralism existed with plaintiffs able to choose to which court they want to take the case and with the court officials free to draw from this or that line of Islamic jurisprudence. This degree did much to limit these. Together with it, certain acts by the CUP meant that the authority of the 'millet' clergymen was somewhat diminished as well, with more control given to the state in recording and approving marriages. That said, this does not mean a radical break, since these changes often did not concern the legal rules at all. There were still multiple courts applying different sets of laws largely derived from different religions. While the Islamic law was now codified and clearly set out for all judges to follow, it was still Islamic law, though 'modernised' at times by drawing from multiple schools of jurisprudence. The Treaty of Lausanne in 1923 did not do much to change this either. Though it basically meant the Western states now recognised the new Turkey, to be a republic within months, this new Turkey was not as yet all that new. The Sharia courts still remained and so did legal pluralism. In fact, one article of the Treaty in particular guaranteed the freedom of minorities in Turkey (read non-Muslim minorities as before) to apply their own religious laws to their own cases.
All this changed in 1926 when a rapidly secularising Turkey legislated a new Civil Code largely translated from the Swiss one. This removed all references to Islam, raised the age of consent, formally banned polygyny (rarer among Turkish-speakers than the Arabic regions in the Ottoman Empire anyway), and so, it was quite a case of Westernisation. The new Civil Code of 1926 also bypassed the Article 42 of Lausanne. Jews, Armenians and Greeks of Turkey were asked and accepted (how willingly I would not know) to renounce their right to use their religious law and accepted that as Turkish citizens, they could take their cases only to secular courts of the state. This meant that one of the last remnants of the millet system thus disappeared in Turkey. Today, it is still common among Turks to have their marriage first 'approved', as it were, by an imam and then by the state. The rules that these imams follow are naturally Islamic and closest to the late Ottoman practices. But this is neither illegal nor has any legal backing. Nobody faces any legal consequences for walking away from an Islamic marriage contract, besides, depending on the location, the good old social pressure.
I do not know if this was enough to answer all your questions, but I hope to have been able to answer at least some of your questions as they related to Turkey. I hope this helps!
Sources:
Avi Rubin, Ottoman Nizamiye Courts: Law and Modernity (New York: Palgrave Macmillan, 2011).
Tuba Çınar, 'Tanzimat Sonrası Gayrimüslim Osmanlı Vatandaşlarının Aile Hukuku: Evlenme ve Boşanma', Journal of Eurasian Inquiries, VII, 2 (2018), pp. 106-152. Available online at (Turkish with an English abstract) 610710 (dergipark.org.tr)
Mehmet Akif Aydın, 'Mecelle-i Ahkam-ı Adliye', TDV İslam Ansiklopedisi, 28 (2003), pp. 231-235.
Mehmet Akif Aydın, 'Hukuk-ı Aile Kararnamesi', TDV İslam Ansiklopedisi, 18 (1998), pp. 314-318.