Sajda-e-Sahw

Q: In Salaah, I recited in my last rak'aat  "Ihdina siraatal mustaqeem". But when I tried to do the Qaf with kasra it was like kaaf and so I recited it again, but this time the ta in Al-Mustaqeem was not properly audible I think, but I moved my tongue to say it and I guess I now think the second time I recited it, it was acceptable - but at the time my mind was like blank, I thought of both carrying on and saying it again and as I was quite pressured because I did not want to remain silent without reciting anything I said it again for a third time, but now I wonder is my prayer invalid because both times when I recited after the initial mistake were acceptable, so is it like I made a purpose addition in my Salaah or am I excused?

Q: Does repeating Surah Fatiha in the 3rd or 4th rakaat require sajdah sahw according to the other view in the Hanafi madhab that to read Surah Fatiha in the last two rakaats is also Waajib as this is relayed from al Hasan from Abu Hanifa and preferred by Hanafi ulama as Ibn al Humam and al Ayni.

Q: If one mistakenly recites the dua of tashahhud audibly in salaah, is one required to perform Sajdah Sahw?

Q: In order to prevent my cough in Salaah, I halted for the duration of three subhaanallah. Should I make sajdah sahw?

Q: One read more than the half of surah al Fatiha in the 1st rakah, then doubts whether he recited the beginning part correctly. If he re-starts from the place he doubts (and thus repeats a half or more of the whole surah) does he need to do Sajdah Sahw? Thus does repeating a half or more due to a doubt whether one recited correctly or not necessitate sajdah sahw, or does sajdah sahw become waajib only if one forgetfully repeats a half or more?

Q: I started salah with takbeer tahreema, however after a few seconds I remembered that I have done the wrong niyah, then I stopped and started my salaah again with takbeer e tehreema. Do I need to do sajda e sahu or not? When does it become obligatory to sajda e sahu?

Q: What is the reason that if in the first or second rakaat Surah Fatiha is repeated twice (or half of more) it does require Sajdah Sahw, but if it is repeated in the 3rd or 4th rakaat, it does not require Sajdah Sahw?

Q: If one repeats Surah Fatiha in the 3rd or 4th rakaat of a fardh Salaah, will sajdah sahw be waajib? 

Q: Will sajdah sahw be performed when missing out a wajib in sunnah and nafl prayers also?

Q: Can you please teach me the method of sajda-e-sahw?