In "I came home after school", the "home" functions as an adverb(ial). But what if the subject is "he or she", is it still "she came home after school"? It's not "she came to house" or "she came to home" right?

In "I went to the Church on Sunday", does the sentence still have the same meaning even if the definite article "the" is omitted?

e.g. "I went to Church on Sunday" => Does this sentence make sense without the "the"?

Thanks in advance.
Yes, very well explained.
He went to hospital

Actually, Coachpotato, this third example is one I don't think I've ever heard said by any native American I know. We tend to say, "He's in the hospital"... or, "He's hospitalized."
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Native speakers correct me if I'm wrong. But as far as I know if you say 'I went to the church' that means that you didn't go to a religious service, while if you say 'I went to church' means you went to a religious service.

The same happens with other words such as prison, school, university, hospital ... You say 'He went to the prison to visit his brother' but 'The thief went to prison'. In the first example he is not a prisoner, just a visitor.

Another example: He went to hospital / He went to the hospital. In the first example he is ill or injured so he is in hospital, while in the other one he is not ill, he is there as a visitor.
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It's true that I went to church is only used in the context of going to a religious service. But I went to the church doesn't mean you didn't go to a religious service. It covers all church visits.

1. I went to the church. I was ten minutes late, and the service had already begun; so I slipped in quietly and stood at the back.

Similarly with 'I went to the prison/school/university/hospital': there are contexts where 'I' could be a prisoner, schoolboy, student, malingerer, etc.

(He went to hospital may be more familiar to BrE than AmE speakers.)

Yes. Within this group of expressions, the only one that differs significantly when American and British English are compared is "to hospital", which doesn't occur in American English, because at the time of the founding of the country there was only one hospital. So if a person "went to the hospital", the place was uniquely identified. No one ever needed to ask, "Which hospital?" So another version without the article would not have been needed. Emotion: smile