Sajda-e-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?

Q: A person doubts whether he is in the 3th or 4th rakaat, and in his mind he has no clue which one it would be. Thus he takes the lesser amount. Should he still sit after the 3rd rakaat and make tashahhud, as there is a possibility that it is the 4th rakaat?

Q: If someone leaves out a sunnah of the salaah or commits a makrooh action in salaah, will it be necessary for him to repeat the salaah? What if the time for the salaah has already finished? 

Q: I was praying my Fardh Fajr Salaah and I did not recite loud like I do in the loud prayers and more like how I recite in the quiet prayers and so I continued reciting how I was so as to keep consistency in the salaah. At the sitting position in the second rak'ah, I said up to "Ashhadu anna Muhammadan 'Abduhu Wa Rasooluh." and said "Assalaamu 'alaykum wa Rahmatullaah" to my right then faced forward and prostrated (I intended to do the two prostrations of forgetfulness for not reciting out loud like I usually do for Fajr Fardh). During this, I got up from prostrating and raised my index finger and was about to start reciting "Attahiyyatu lillaahi Was-Salaatu Wat-Tayyibaatu." But then, I was confused whether I prostrated once or twice, and I leaned to the decision that I had only prostrated once so far and so I said "Rabbighfirlee" three times and prostrated for what I assume to be my second prostration. I sat back up and said the Tashahhud, Durood and Du'a, then I said both Tasleem. Now I wonder is my salaah valid?