Jamaat Salaah and Imaamat

Q: Does a muqtadee have to recite the takbeers in salaah when going from one posture to another?

Q: If in congregational prayers and Jumu'ah and Eidain, the Imam is in the indoor hall of the masjid and saffs are made behind him and the door of the hall is closed but not locked and saffs are also made outside, but there is a distance of 3 saffs between the last indoor saff and the first outdoor saff, are the congregational prayers or Jumu'ah or Eidain prayers valid?

Q: Can a person who has a lisp or a problem with any other letter be made imam for salaah in a masjid?

Q: In a small Masjid, the Imam used a sutrah while leading the jamaat (it is a common practice in some places to do second or third jamaat if the main jamaat is missed). Is it permissible to pass in front of people who missed their rakaat with the Imam in these second/third jamaat are completing their prayers. Will they still be considered to be behind sutrah even if Imam has completed his own Prayer?

Q: Is it necessary for the imaam to make intention for the people behind him? Example if there's women in the jamaat, does he have to specify he's leading the salaah for women?

Q: My two daughters are haafizah. Can my two daughters pray together the Taraweeh Salaah while one of my daughter recites the Quran and the other rectifies the mistake? Is there any possibility that only the two of them perform the salaah like this for revision purpose? This won't be a congregation since only the two of them will perform the salaah like this.

Q: My sister and I are haafizah of the Quraan Shareef. Is there any possibility of me and my sister reciting Quraan in taraweeh salaah for revision purposes? If there is a possibility, then what's the correct method to do this?

Also, if one of us makes a mistake during congregation salaah, can the other one rectify the mistake? 

Q: If there is only one child for salaah, must he stand in his own saff or must he stand in the adult saff?

Q: Is azaan mandatory in a small office mosque where 2 or 3 jamaat prayers are held and not all? The above mentioned mosque has no speakers, no fixed imam and muazzin, whenever multiple people come then they pray in jamaat.

Q: A late comer joins me in salaah while I'm performing my sunnah salaah. Is it permissible for me to change my intention of performing sunnah salaah alone to performing in jamaat?