Practising Deen entirely from the time one accepts Islam

Q: At the time of the Prophet (Sallallahu Alayhi Wasallam), some laws of Islam were revealed in steps, for example regarding the prohibition of alcohol. I saw that a part of a Hadith of Aisha (Radiyallahu Anha) says that "If the first thing to be revealed was: 'Do not drink alcoholic drinks.' people would have said, 'We will never leave alcoholic drinks'". My question is: is there any consideration given also to the situation of converts to Islam in our time, or do all rules of Islam become binding on them directly? For example, a woman that has lived all her life “freely” by travelling here and there, speaking to people of the other gender etc, will niqab and purda become obligatory on her the same moment she converts to Islam or will it be permissible for her to follow some more lenient rulings during a transition period, e.g. by only wearing a scarf covering the hair?

Remarrying if one finds a suitable partner

Q: I am 30 years of age and divorced with 2 kids a girl and a boy. I have been a lone parent for over 8 years now and I really feel that I need a partner and at the same time I worry for my kids too. My parents don't want to get me remarried because of the children. My mum worries too much about the kids that if their own father left them then how can a step father take care of them. I agree with her too but I am there for my children and always will be, they are my life, but there are some good people out there too. A father can leave his kids but a mother can never leave her children. Could you please tell me a dua or a wazifa that I can read so that my parents think about me and my children, accept that fact and I get a very good life partner that will accept me with my 2 kids and fulfil the duties of a real father.