The plane that he was scheduled to take to Hawaii was delayed.
You cannot omit ‘he’. There is an expression to take a plane to. He( a man) was scheduled to take a plane By the way, this construction seems correct to me:
The plane was taken to Cincinnati (by Daniel)–passive form
But the sentence:
The plane that was scheduled to take to Hawaii was delayed- I believe, it’s not corect. However:
The plane (that was) scheduled to be taken to Hawaii was delayed-is correct, to my mind.
Do you have some money?
It is fine. I’d rather say, in this particular case it is tantamount to Do you have any money?
Now let’s analyse the two sentences given below:
Can you give me some money?
Can you give me any money?
They are not identical in meaning. When you ask your friend : Can you give me some money?
You know that he has money.
When you ask: Can you give me any money?
You are not sure whether he has any money or not.
I don’t like some of the books.
It is grammatically correct. By using ‘some of’ you specify that among certain choice of books(presence of ‘the’- the books) some of them you don’t like.