Jamaat Salaah and Imaamat

Q: Is it permissible for me to perform the zuhr salah late at home just during the winter, rather than having to pray every single day at school during the winter?

Q: Please advise on the following:

A) When making Salaah and if coming up from ruku, where one is supposed to have said,  SamiAllahu Liman Hamida, one said Allahu Akbar,  is the Salaah valid?

B) When the Imaam is in Ruku,  and the person joins the Salaah by making Takbeer Tahreemah,  folds his hand and thereafter recites Allahu Akbar again
and goes into ruku to join the Salaah behind the Imaam and make it for the Rakaat, Is the Salaah valid?

C) If one joins the Jamaat of Salaah when the Imaam is in Qadah, and one reads Takbeer Tahreemah,fold one's hands thereafter reads Allahu Akbar again,
and goes into Qadah to join Salaah, Is the Salaah valid?

D) What would be the best and most correct option of joining Salaah at the times mentioned in B and C above?

E) What is the status of reciting after the Imaam during Salaah when the Imaam goes into ruku, comes up from ruku, goes into Sajdah,  comes up from
Sajdah, basically after all the Takbeers and going into the next posture.

F) If after the Imaam comes up from ruku, saying Samiallahu Liman Hamida, What does the Muqtadee do? Does he also says Samiallahu Liman Hamida in
keeping with the above ( question E)

G) In also keeping with the above in question E,  if one recites Allahu Akbar instead of Samiallahu Liman Hamida, Is the Salaah valid?

H) In Qadah Ulaa or Qadah Akheera,  whilst reading Tashahud,  if one gets confused or makes a mistake after Saying  Ash Hadu Allah Illaha IllahAh, where one is supposed to raise one's index finger,  and where one already raised one finger,  but happen to go back to correct the mistake and start from the beginning again if one was confused, Should the index finger be raised again ( for the second time in correcting the mistake)?

I) What is the status of the raising of the index finger whilst in Tashahud?

J) If one joins Salaah behind the Imaam whilst the Imaam

J1) is in Qiraat (Busy reciting Surah Fatiha or  a Surah) of first Rakaat
J2) Ruku of the first Rakaat

When would be the correct time to read Thana?

K) If one misses one or two Rakaats of Salaah behind the Imaam,  when should one read Thana?  When joining the Salaah or when standing up to complete the
missed rakaats after the Imaam finished Salaah?

L) What is the correct procedure of completing Salaah if one missed 3 Rakaats of a 4 Rakaat Salaah?

M) What is the correct procedure of completing Salaah if one missed 2 Rakaats of 3 rakaat Salaah?

N) In Wudhu, what should one put water into the nostrils amd when should Khilaal of the beard, fingers and toes be made.( If the full and correct procedure of Wudhu with full Sunan be given it would be appreciated)

Q: If a group of people, who are not musaafirs, come late to the musjid after the first Jamaat is over, will it be better for each person to perform his Salaah individually or for them to make a second jamaat? Will the same ruling apply if they perform their Salaah in the sehn of the musjid? (i.e. will it be better for each person to perform his Salaah individually or for them to make a second jamaat in the sehn?)

Q: If an imam makes a mistake and you don't correct him out of shyness or other reason, is it a sin?

Q: If azaan has been given for salaah, so it is compulsory to make jamaat?

Q: When joining salaah late after takbeer, after I have put my hand on my belly, how should I recite thanaa?

Q: What is the correct way to pray the Salats of Zuhr and Asr behind the Imam? Also, please, explain what is the correct way to perform the third Rak'ah of Maghrib and third and fourth Rak'ah of Isha behind the imam. Should a Muqtadi (person praying Jamaat behind Imam) recite Fatiha and Surah in the first two Rak'ahs of Asr and Zuhr and then recite Fatiha only in the last two Rak'ahs of Zuhr and Asr? Also should the Muqtadi recite Fatiha in the third Rak'ah of Maghrib and in third and fourth Rak'ah of Isha or should he stay quite? You I have to read inni and sana before surah fatiha in jamaat and in sunnat prayers shall I recite inni and sana? While performing prayer alone of maghrib what to recite in the third rakat?

Q:

1. If there are women following the Imam, does he have to make a specific niyyah for them?

2. If he makes general niyyah for all those following him, will it suffice?

3. If he didnt know there were women following him, will their salaah be accepted?

4. If he knew but didn't make intention for them, will their salaah be accepted?

Q: I want to know what should be done if you miss 1, 2 or 3 rakaats of a fardh Salaah?

Q:

1. If an imam has no duties except leading farad prayer, is his salary a price/ reward for his salaah? Is it not worshipping for money? Is it halaal to charge for what has been obligated by Allah Ta'ala?

2. If you employ a Hafiz to lead taraweh prayer in Ramadan, is his worship (for money) permissible and is the worship of his followers, behind him, acceptable before Allah Ta'ala?

3. When children are taught Quran by a paid tutor, is the teacher allowed to accept this material reward and still be 'khyrokum munn ta allaml quraana wa allama hoo'?

4. If it is not permissible to trade your (farad or sunnah) Ibadat for money/ receive salary, how should Imams of masjids and tutors run their household and kitchen?

Please advise in full detail with references from Quran and Sunnah.