Answer:
(Fatwa: 1129/L=291/tl=1431)
(1) Yes, your salah was valid. If you recite اللهم صل على محمد at this time it is far better.
(2) After offering the fardh of Fajr if there is time to offer sunnah it is not lawful for you to offer sunnah immediately. However when the sun rises and makrooh time is over then you can offer sunnah.
(3) I could not find the said virtues of reading third kalimah, durood and istighfar for six months after Fajr and Asr salah. These zikrs should be recited forever; it has always been in the practice of our elders.
(4) I could not find its detail as well.
(5) If you follow sunnah in eating, drinking, sleeping, walking etc it is hoped that Almighty Allah will make it easy for you to practice on the other sunnah acts.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband
