Witr and Nawaafil

Q:

1. If one is late for fajr jamaat, and performing the sunnats will result in missing jamaat, what should one do?
2. Can the sunnats of fajr be performed after the fardh? I have noticed some brothers doing this?

Q: What is the ruling regarding lying down after the two sunnats of fajr in the Hanafi madhab?

Q: What is Salaat-ut-Tasbeeh and when and how to perform it?

Q: What is the difference between Qiyaamul Layl and Tahajjud? Is it necessary to sleep before offering Tahajjud or can one perform it immediately after Esha?

Q: If one does not know dua e qunoot what should he recite in place of it?

Q: Please can you advise how many rakaats to be read for Tauhajud and can one recite any surahs and also how many rakaats to be performed together?

Q: I heard that if one prays two rakaats salaat e Haajat at Tahajud time and in the first rakaat after sura e fatiha one recites Rabbana Ateena
fid dunya Hassanato Wafil Aqirat e Hassanaton Wa Qina Azaabun Naar. Only this Ayat countinously as much as he can if possible 1/2 - 1 hour and do the same thing in the second Rakaat and after finishing the salaat and salaam and recites the same Ayat unlimitedly while sitting and after that he prays for any purpose it will be accepted, when I heard this I decided to recite this Ayat for at least 5 minutes in both Rakaats if I could'nt recites for One hour.  Please Advice me on this. JazakAllah.

Q: I have deep doubts regarding the authenticity of witr salaah of the Hanafi Madhab. I have asked a Sheikh and he told me not to read in that manner. Can you mention to me few authentic Hadeeth regarding this issue. 

Q: What is the time difference between rakatul fajr and salaatus subhi? Should the sunnah be considered as optional?

Q: Is ishraaq and chaast salaah the same or we should read both because I am regularly reading ishraaq but chast I read some times. Someone said it is the same, if you read it in the early morning it is ishraaq and if you read it later than it is called chasit. Please explain.