Jamaat Salaah and Imaamat

Q: Should a masbooq stand up for completing his missed rakaah after the imaam has done the first salaam, or should he wait for the imaam to also complete the second salaam?

Q: I missed the first rakaah in a jamaat salaah. When the imaam said salaam to the right, I mistakenly also made salaam, but I did not do salaam to the left. Did I have to do sajdah sahw after completing my missed rakaah because of this mistake?

Q: When you follow the imam in zuhr and asr salaah, and the silent rakaats of the other salaah, what must we read?

Q: We are hostellers, 3 friends (age 20-22) in one room and we have kept a separate place on the balcony of our room for jammat namaz where 4- 6 people (or more) can easily adjust without any problem. I heard a hadith that one who does not offer jammat salaah if he/she can, when he/she will be inside grave, his/her face will be moved away from the qiblah.

I told my friends about the hadith and one of my friends asked me who will be the imaan from amongst us since we all make mistakes. If anyone of us will be an imaam and if he makes a mistake, he will get the sin of the muqtadi's (people standing behind the imaam) also.

My point of view is that no one is perfect but we can try. If with full attention, concentration, seriousness, students like us would like to lead the jamaat of other students (even after knowing that we are not perfect), would it be wrong? 

Q: If the imaam does not recite correctly, will it be ok to perform salaah behind him or should I perform salaah at home in such a scenario? 

Q: The place where I live is a very cold place so the imam of the mosque always wears normal socks and does masah on the socks. Is it better to pray behind him without doubting or pray behind him and repeat the namaz make jamaat at home with one's family members? Which option do you recommend?

Q: There is a masjid inside a university where many Muslim students live, but it often does not have any jamaat salaah on Sundays, though the Friday prayer is held there.

An imam is appointed for the masjid, but he often does not come for Fajr, Isha and prayers on weekends (maybe because he lives far from the university). When the imam is not present, anyone leads the prayer. Is it correct to start a 2nd jamaat after the imam has already led the 1st jamaat salaah?

Q: If the Imaam stands for the 5th rakaat, will the muqtadi stand with the Imaam?

Q: Can an old man who performs salaah on a chair lead the jamaat salaah in the Musjid?

Q: Two people were performing salaah with jamaat. Thereafter, a second muqtadi joined the jamaat, but the first muqtadi did not move back to stand with him behind the Imaam. In this case, should the Imaam move forward?