Usage of the word 'The' [duplicate]

AmEng speakers do NOT use definite articles all the time; whether we do or not depends on what we want to say, and how we want to sound saying it. In particular, the use of the definite article with the present tense of the verb "to be" depends (in the words of a famous American) on what your definition of "is" is. Several of your example sentences sound distinctly unnatural to my USAite ear. Here are my suggestions based on my own usage:

School:

• He is in school. - He is a student; specific time does not matter. Perhaps it's Friday night and he's partying right now.
• He is in the school. - This does not sound natural at all to an American ear.
• He is enrolled in the school. - He is a student.
• He is at school. - He might be a student OR a teacher, but he is on the premises at this moment.
• He is at the school. - "The school" is a local landmark, and he's there right now.

Hospital:

• He is in hospital. - He's an inpatient. This is valid, but not usual American usage. Anglophiles (Americans who like to drop Briticisms into their speech to appear more sophisticated) will sometimes use this.

• He is in the hospital. - He's an inpatient.

• He is at hospital. - We don't say this.

• He is at the hospital. - He might be an outpatient, or he might work there; either way, he's there right now.

Church:

• He is in church. - Services are in progress right now, and he's there.

• He is at church. - Interchangeable with "in church".

• He is in the church. - He's inside the building; no information is conveyed about what he's doing there (he might be polishing the floor, for example.)

• He is at the church. - He's on the church grounds, not necessarily inside the sanctuary.

University/ College:

• He is in university. - Americans don't usually say "in university"; "in college", however, means that he's a student.

• He is enrolled in university. - He's a student.

• He is at university. - He's a student. This is much more common than "in university", for some reason.

• He is in the university. - Again, we don't say this.

• He is at the university. - The university is a local landmark and he's there now. (Who is he - student, professor, tourist? Not enough information.)

Prison:

• He is in prison. - He's a prisoner.

• He is at prison. - We don't say this.

• He is in the prison. - He's inside the building. He might be a prisoner, a warden, a visitor...

• He is at the prison. - He's on the grounds, not necessarily inside the building - he might be waiting in the car while his wife visits her brother.

In AmE, for your examples:

• No. He is in school. (enrolled as a student)

• Yes. He is at the school. (for some different reasons)

• Yes. He is in the hospital. (as a patient)

• Yes. He is at the hospital. (visiting somebody) or could be a patient, too.

• No. He is in church. (to pray)

• Yes. He is at the church. (for some different reasons)

• No. He is at/attending college. (as a student)

• Yes. He is at the university. (not as a student)

• No. He is in/at college. (as a student)

• Yes. He is at the college. (not as a student, the physical place)

• No. He is in prison. (as a prisoner)

• No. He is in the prison. (not as a prisoner)

The general rule is 'in X' for being part of the institution, but 'at the X' or 'in the X' for being physically related to the building (but note that this doesn't always work: 'in the hospital'). And the institution is 'in college' even if it is nominally a university.