Writing and saying talaaq three times

Q: I wrote three times I give divorce my wife in front of my mother but my wife don't know about that but we again together. Then my wife asked divorce I say 3 time divorce and same time wrote 3 times I gave divorce and 2nd or 3rd day in front of lawyer I sign on divorce paper again but within 15 days we again together. After that we sit together and say each other we are doing nikah again. So kindly let me know are we still husband and wife and now we have a son also. Please guide me thanks.

Invalid nikaah

Q: I'm from India. 11 years ago my sister loved a Muslim boy who was 2 years younger to her and was a student. When this was disclosed in front of my parents, they asked her to stop all this in every possible way, that is by explaining her the difficulties she will face by marrying that boy, by telling her that if this matter will come out they will loose their respect in the society, by scolding her, by keeping an eye on her, even by beating her. But she and that boy didn't understand as they loved each other madly. Then my sister ran away with that boy and they conducted nikah in front of qazi, a non Muslim boy and a Muslim boy for whom we have doubt that he was of less than 18 years of age (Allah knows the best). No wali was present. Then my parents begged her to come back and they will marry her off with that boy in front of the society. When she and that boy came back, the boy's family said that they will not marry their son to my sister. Our father took us to Saudi Arabia, there he threatened my sister to forget that boy and live peacefully as someone told him that, that nikah was not valid as it was conducted without wali and the witnesses were not fulfilling the Islamic standard. Now everyone thought that, that nikah was invalid including my sister, so we didn't ask for talaq from that boy. After 2 years my sister got married to a nice man with her consent. She is having two kids with that marriage. That man don't know about my sister's past. It's been 9 years now. They are happily married.

Now we are in a big confusion that the previous nikah was valid or not? Is the present nikah and kids valid for her? Is a nikah conducted without wali considered as valid? We did not ask any mufti earlier as we thought that a nikah without wali is invalid. If this is not so then this another marriage has been conducted due to lack of proper knowledge. What is the ruling regarding this matter. Please help us.

Doubts regarding a Hadith

Q: I have a question. There is a hadith that a sinful woman got Jannah because she quenched a dog's thirst. Now my question is today, so many kafir people are donating money and we heard about the hardwork of Florance nightingale and Mother Teresa. What about them? We didn't hear that she used to worship Allah or repent. So what is the objective of this hadith? Even if someone is kafir or dont pray would they have hope to get Jannah?

Breaking a promise

Q: A Moulana was doing a bayan on the internet and the Moulana said how much of you miss salaat some times, so I raised my hand. He was on the internet talking and I was listening on my phone. Then he said how much of you will make sure you will not miss namaz again so I put up my hands and then the Moulana said that we need to put in our minds that when we put up our hands, the angels were witness that we put up our hands. From today, now insha Allah I try to read my 5 times namaz. If I miss a salah, not on purpose but some times for fajr if the time is near to end and I put my alarm and I miss it or I said that I'll wake up and when I wake up time was up. Do I have to give kaffarah because I raised my hands when the Moulana said who will not miss salah from today? Is that a promise?