What is the difference in meaning between “He wanted her to buy the book” and
“He hoped her buy the book”?
Can “He wanted her to buy the book” be used in the situation, “She did not intend to buy the book. He asked her to buy the book”?
Can “He hoped her buy the book” be used in the situation, “She tried to buy the book. He cheered for her to buy the book”?
Can “He hoped her to buy the book” be used in the situation, “She did not intend to buy the book. He cheered for her to buy the book”?
Your sentences with “hope” are not grammatically correct. Unlike “want”, hope doesn’t take an indirect object. However we can hope for someone to do something.
I hope she will buy the book.
We also commonly use the present tense with “hope”, even for future actions
I hope she buys the book.
If talking about a past hope, what we hope to happen may or may not be in the past, so we have to conjugate it separately.
I hoped she would buy the book (and she did). (past hope, past action)
I hoped she will buy the book (but now I don’t think she will). (past hope, future action)
The difference between “want” and “hope” is subtle and internal and difficult to define. I would recommend using a translation dictionary in the hope that your native language has separate words for these.
However, to give it a try: To want is a general way to express a desire for something, e.g. “I want a cookie”.
Meanwhile, to hope is akin to wish, that is, to want something without expectation that it will happen, or without any power to make it happen, or by appealing to someone else (including a deity) to make it happen, e.g. “I hope my friend brings me some cookies”.