Jamaat Salaah and Imaamat

Q: Is it preferable for the Imam to lengthen the Ruku' briefly when hearing someone entering the Masjid to join the Salaah?

Q: I visited a certain website, according to them hanafis can't pray behind Imams of the haramain if they don't take care of the masaail in wudu as hanafis do i.e they should do masah of head to more than quarter of the head, if they don't do we can't pray behind them. I think this is not good, at the time of Sahaba there would not have been such an issue as to not offer salah behind any specific sahabi. Please clarify.

Q:

1. List the circumstances under which an Imam who is the most knowledgeable may in his own presence permit a man of lesser knowlege to be Imam for that Salaah; meaning that how is it possible for an Aalim to permit a hafiz to be Imam when the more knowledgeable person has the responsibility by virtue of his greater knowledge to correctly be the appropriate Imam?
2. Does the Imaamat of the unappointed Imaam, despite it being out of place, does the Salaah of such an Imaam and that of those musallees following such an unappointed Imaam, become an invalid or null and void Salaah?

Q: The Imaam of my Musjid trims his beard to less than a fist length. Should I pray salah after him or not?

Q: My question is that we read the Alhamdu shareef in our namaz. When we read namaz in jamaat then do we need to read the Alhamudu shareef or not? 

Q: I heard that it is makrooh to perform Salaah behind an Imam who shaves his beard or trims it less than one fist? Is this true? If so, is it better to pray alone if there is no Imam with a Shar'ee beard present? Or is it not sinful to pray behind such an Imam?

Q: Do I also have to repeat my Asar salah if I read it in shafi time with a shafi Imaam?

س: لو شك المأموم في الركعة الثانية أنه قرأ الفاتحة في الركعة الاولي ام لا,ماذا يفعل؟

Q: I joined salaah jamaat at 5:17. Jamaat starts 5:15 at the end I didnt know much rakaats I read but because I joined at that time I regarded it as 4 rakaats. Is salaah valid?

Q: If a person does not go to a Musjid, and performs Salaah at home with his wife behind him, would he be absolved of the Wajib of Jamaat Salaah?