Are you sure the school is the direct object?
Yes, he is 'going' but he is not 'going his school'. The 'to' means he will eventually end up at school.
An example makes this more apparent: He watched a movie says the movie is what he is watching, but before this he must go to the cinema. The cinema and the movie are different: he goes (intransitive) to the cinema and watches (transitive) the movie.
Hopefully this explains it.
Break into is a transitive verb. This is what the Merriam-Webster Unabridged says. Other dictionaries seem to differ, but in this answer the verb will be used in a transitive sense.
Specifically, it is a prepositional verb because the verb + preposition make one meaning-unit. (A prepositional verb is not a phrasal verb, even if some dictionaries wrongly list break into with phrasal verbs. (There are tests to distinguish the two types of verbs; I don't want to overlong this answer with them, but I can provide).
Without an object, the sentence is incomplete and thus ungrammatical:
ungrammatical without an object:
*He broke into.
grammatical forms:
active:
He broke into the house
passive:
The house was broken into by him.
Note the sense of action or motion or direction (He broke into the house).
Notice that break into cannot always be used in the passive. It is precisely when the verb does not have a sense of motion/action that this is the case.
He broke into a sweat.
*A sweat was broken into by him.
The audience broke into applause.
*Applause was broken into by the audience.
*A gallop was broken into by the horse
Last, another transitive verb, composed of one word, can substutute for break into: burgle. (Note there are no exact synonyms and let's not get into legal definitions.)
Best Answer
I dreamt a strange dream.
The verb dream can be used as a noun, transitive verb, or intransitive verb. In the above sentence, it's a transitive verb; the subject is I and the direct object is "a strange dream". The sentence, though grammatically correct, sounds old-fashioned. Usually, you say "I had a strange dream.
All his friends laughed at him.
The phrasal verb in the sentence is a transitive verb; the subject is "all his friends and the direct object is "him".
The watch cost nine hundred dollars.
The verb is transitive; the subject is "the watch" and the direct object is nine hundred dollars.