Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The ruling about a photo studio whether it is permissible or Haram depends on the ruling on taking pictures and photographs, and the kind of photographs the photographer takes, and whether these photographs are free from forbidden things.
Detailed Fatawa had been issued on the ruling on taking pictures: Fatawa: 81245, 83020 and 83242.
However, if we examine the reality of the photo studios we notice that most of them do the following:
1) They develop the films given to them. It is known that some of these films contain Haram pictures, like pictures of naked women or nearly naked women, or pictures of naked men or nearly naked men. It is not permissible to develop such pictures or take such pictures, and the money earned from this is Haram.
2) They take pictures of marriage celebrations or develop the films containing such pictures. Most of these pictures contain pictures of women not dressed respectfully, with make up, showing parts of their body which are not Halal to show except for a husband or Mahram, and even worse, showing parts that should not be seen even by a Mahram. So it is not permissible to take such pictures or develop them, because they are a means of propagating mischief and spreading adultery and fornication, and helping in mischief and falsehood.
3) They take pictures of celebrations in which there are songs or music, or pictures of festivals and so on, and develop pictures taken from these occasions which are not free from women who are not properly or respectfully dressed.
In addition to this, a person who takes pictures of these places is committing other Haram things like listening to songs and music or watching female dancers, etc… according to what is present in the celebration or festival.
For more details and benefit you can refer to Fatawa: 81545 and 81239.
There is no doubt that taking pictures of such celebrations and festivals is not permissible, and it is not permissible as well to develop such pictures. Let alone, if the studio deals with cinemas or theatres, etc., and the forbidden things that occur in such celebrations are not hidden.
Based on the aforementioned grounds, we would say: If the photographer can limit himself to taking pictures of what is permissible and to developing the pictures that are permissible, then he can do so, otherwise he has to close his studio, and look for permissible work, despite the fact that limiting himself to what is permissible is very difficult and nearly impossible. We remind you of the Saying of Allah (interpretation of meaning): {…And whosoever fears Allâh and keeps his duty to Him, He will make a way for him to get out (from every difficulty). And He will provide him from (sources) he never could imagine.}[65:2-3].
It is permissible to take pictures of things that have no soul, like trees, rivers, and mountains, and of religious celebrations that have no music, or religious conferences, or news that is beneficial for the Muslims, taking into account religious requirements. May Allah enable you to do whatever He likes and is pleased with.
With regard to the fourth question, there is no harm in taking pictures of things that are needful, or for a correct purpose such as for archives, etc. as long as you avoid taking pictures of Awrah (parts of the body that must be covered).
Allah knows best.