1- It is not permitted. 2- It is like the previous issue. 3- Yes, you can ask all religious lawful matters from Allah.
Perform the number of prayers that you are certain you have missed with the intention of obligatory qaḍā and if you want to perform more than that, perform them with the intention of precautionary qaḍā.
The time of the morning nāfilah starts before the Fajr prayer , f r o m the Fajr adhan until the appearance of redness in the east, and it is possible to perform that immediately after the night prayer.
The Paternal homeland of a person is not considered as the homeland of that person unless he/she stays there continuously for a long time like one year.
If a person wants to stay 10 days or more in a place, in this case prayers should be performed complete and the person must fast. And if this person wants to stay less than 10 days then prayers should be performed shortened and the person cannot fast. The beginning of 10 days is from the moment of entering the destination, for example from noon of the first day of arrival until noon of the next day is considered as one day.
If other people consider you just then there is no problem for you to be Imam of congregation.
Attending their Friday Prayer with the intention of creating a great unity among Muslims is good and suffices in lieu of noon prayer on Friday. Furthermore, under such conditions, there is no issue with prostrating on carpet.
It is not necessary but it is better to correct their mistake.
This act is makrūh (abominable) unless this is the only way of having presence of the heart (full concentration).
It is permissible.