Learn English – Use of the definite article “the” before “church”

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 the present-day style of the US Navy (and as far as I can tell also the Royal Navy, though I cannot find a suitable link), the definite article is inserted only when giving the type of vessel— never directly before the vessel's name itself. Thus, the publicity piece entitled “Nimitz Arrives Home” opens with

More than 3,000 Sailors on board the aircraft carrier USS Nimitz …

but subsequent references are bare:

While at sea, Nimitz completed approximately 374 launches and recoveries …

"I am very proud…" said Capt. Jeff Ruth, commanding officer of Nimitz.

In vernacular English the article is both prevalent and rather longstanding in use. Early in Shakespeare's Macbeth, the first witch tells a tale:

Her husband's to Aleppo gone, master o' the Tiger:

Or consider the innumerable examples in Purchas His Pilgrimes, a 1625 book "contayning a history of the world, in sea voyages & lande-travells by Englishmen & others," at least six of which lie in this excerpt:

Why this became conventional in English is difficult to say. Perhaps it became natural because the London would clearly refer to something named after bare London— meaning the city— General Slocum was a disaster, but nothing like the General Slocum. Many large or important physical objects and features idiomatically take the article, and a ship big or important enough to take a name might be expected to do so. But articles are highly idiosyncratic; we weekend on the Isle of Wight but on Isle Royale, we sail on the Great Bear Lake though on Lake Ontario, and even climb up the Matterhorn yet up Mont Cervin— the very same mountain, just known by several names.

Proper nouns are particularly twitchy, for not only are names themselves rarely logical (e.g. the people who call themselves Nederlanders we call the Dutch; the people who call themselves Deutsche we call Germans), but the entities they represent may have a preferred “house” style that differs from the styles preferred by other substantially similar entities. Elsewhere I provided the examples of

She is a professor at The Ohio State University. She received her Ph.D. from The George Washington University, and was prepared at The Lawrenceville School.

She is a professor at Kansas State University. She received her Ph.D. from George Mason University, and was prepared at Darrow School.

She is a professor at the University of Arizona. She received her Ph.D. from the College of Charleston, and was prepared at the Milton Hershey School.

Related questions include the following:

1. When to use a definite article in the name of a ship
2. Using the definite article before a country/state name
3. Why use “the” for oceans/seas/rivers etc. but not lakes?
4. Use of definite article before phrases like Heathrow Airport, Hyde Park, Waterloo Station, Edgware Road and Parliament Square
5. Why 'The' is used?
6. Should “the” ever be dropped from the beginning of a name/title?
7. Definite article with proper nouns, titles followed by a common noun
8. Document names and proper nouns/definite articles
9. Definite article before schools, colleges, and universities