Modals.

Hi, I am a student yet. I have some questions about the English Grammar and Vocabulary.

I was studying by the Intermediate Language Practice: English Grammar and Vocabulary by Michael Vince with Paul Emmerson, because I have a test. While studying, I found a interesting question, but no answers. Could someone help me?

The phrase:

Affirmative: Hellen has to study hard.

Negative: Hellen doesn't have to study hard.

1. How can I write this same phrase in interrogative?

2. It will be the same meaning if I write the interrogative as "Must Hellen study hard?"?

3. When I write "Hellen doesn't have to study hard", does the "doesn't" have same meaning as the "needen't" ?

The phrase:

Affirmative: Robert and Marine had to sleep late yesterday.

Negative: Robert and Marine didn't have to sleep late yesterday.

Interrogative: Did Robert and Marine have to sleep late yesterday?

Now, compare with this phrase:

Affirmative: Diane had to eat vegetables.

Negative: Diane didn't have to eat vegetables.

Interrogative: Did Diane have to eat vegetables?

1. If you look at the second phrase "Diane didn't have to eat vegetables", you can notice that Diane is only one person and it means that it is singular. But why do they say "have to" and not "has to"?

2. Is there something wrong in the book or it is like this? Read the Interrogative, they use "have to" and not "has to" for "Diane".

Ok, that's all. I hope to see the answer soon, because my test is tomorrow and I think I am not prepared. I think I will go better if I know about these stuffs.

Thanks for read my questions! Answer me! I need your help!