Jamaat Salaah and Imaamat

Q: If I missed the first rakha and joined in second one. During the salah imam made a mistake and at last did sajda-e-sahw. Should I complete the first rakaat or not?

Q: I want to ask about my prayer. Can I pray at home as my mother is bedridden for the last 5 years and she needs a lot of care the whole day; from eating, drinking, changing, etc. like a toddler. Its very difficult for me to join fard prayer on time. Please advice.

Q: I had missed two rakahs of maghrib in Jama'ah, so I continued to offer them after the Imaam said salaam. But I recited a surah in both the rakahs, thinking that my prayer would otherwise have only one surah recited. Is this correct?

Q: I was leading the Asr prayer and there was only one young boy along with me who stood on my left instead of my right. Is this Jama'ah correct, or should I repeat this prayer?

Q: In few mosques there are arrangements to offer prayer with jamat on 1st and/or 2nd floor along with the ground floor. I heard from some elder person that if the distance from one row (of jamat) to the subsequent row is greater than 2 row's size than prayer of the person of the subsequent row will not be valid. Hence if the roof's height of the ground floor is higher than the 2 row's size then the prayer of the person (offering prayer) in jamat on 1st floor will not be valid. Is this case true?

Q: My query is regarding the hadeeth of the child Sahaabi who performed salaah behind Nabi Sallaallahu alaihi wasallam and then went to his tribe and led the people in salaah.

1. Can the exact hadeeth be given with the references.

2. Is it permissible to use this hadeeth as a proof for a child being allowed to do imamat (albeit for taraweeh)

3. If possible, what is the fatwa of the A'imma Arba'a with regards to the above maslah.

I only ask this as recently in a musjid, naa baaligh children were allowed by the mutawalli of the musjid to lead the taraweeh salaah.

Q: I would like to find out all the Shar'ee laws pertaining to: - Imamat / leading a congregation in Salaah - Non Baaligh child making Imamat - Imam having a beard - Imam not following rules of tajweed. - Imam wearing his pants below his ankles. Please can I also have references for each of the queries.

Q:

1. Is it permissible for a person who is clean shaven (due to medical reasons - acne) to be Imaam of salaah?

2. If yes, would it still be permissible when there are Ulama and Huffaaz who would meet all requirements of an Imaam?

Q: When one misses a rakaat with Jamaat, as one stands up, do you start with Thana or Sura Faatiha.

Q: When namaz is being performed in congregation and I joined as muqtadi after third rakath and after Salam I will have to pray the due rakat, while performing my due rakath can other muqtadi join me which makes me imam to new muqtad?