At school/ in school?

The use of articles before the words like church, hospital, school, university, etc( does the word factory also belong to this group?) is still confusing me. Could you please give me all possible versions for each situation I quoted here in this post?

1. There are many schools and she works in one of them. She works in/at a/the/- school.

2.There are many schools and she studies in one of them.She studies in/at/a/the/-school.

3.There are many schools and she studies and works in one of them. She works and studies in/at/a/the/-school.

4.There is only one school in the area where she lives and she works in it.

She works in/at/a/the/-school.

5.There is only one school and she studies in it. She studies at/in/the/a/- school.

6.There is only one school and she studies and works in it. She works and studies in/at/a/the/- school.

She is at school because she wants to talk to the teacher(I think I should say to a teacher.); She went to the/- school to talk to her son's teacher.

'She went to a school' - If a person isn't specifying the school, am I right?

Can these examples help me to build similar sentences using words like church, hospital, university, etc?

What other possible versions can be used with 'school'?