As you suggest, Christina, need can be used in two different ways.

do not need to

On the one hand, it can be used as an ordinary verb and has the same forms as an ordinary verb. The third person singular ends with an s, and questions and negatives are formed with do. As an ordinary verb, need is normally followed by an infinitive with to:

• He needs to see a doctor. Do you need to see one too? ~ No, I don't need to see a doctor. But I need a good rest.
  
  
• You don't need to be over 21 to go into a pub in Britain, whereas in America you do.

In this sense, when we are talking about necessity, we generally prefer need to / do not need to.

needn't

In the other format, need behaves as a modal verb, like can, could, must should, etc. It has the same forms as modal auxiliary verbs: the third person singular has no s, questions and negatives are made without do. In this format, need is followed by an infinitive without to:

• You needn't bother to change the sheets. I'll sleep in them later.
  
• Need I lock the door when I leave? ~ No, you needn't. Sarah will be home soon.

In this sense, we are talking more about obligation and giving permission to someone not to do something. Note also that as a modal verb it is most commonly used in negative sentences and sometimes in questions.

In your examples, too, Christina, you are talking about obligation on the one hand, and necessity on the other. Compare the following alternatives to needn't and needto in the examples below:

• You needn't come if you don't want to.
  Don't feel obliged to come if you don't want to.
  
  
• You don't need to be a genius to see that it is wrong.
  You don't have to be a genius to see that it is wrong.
  

doesn't dare to - daren't

Dare, meaning have the courage to do something, can also be used in two ways:

* as an ordinary verb followed by an infinitive with to, with s in the third person singular and with questions and negatives formed with do

• He never dares to criticise her for wasting money and she doesn't dare to interrupt him when he's working.

* as a modal auxiliary verb followed by an infinitive without to, with no third person singular s and with questions and negatives without do:

• Dare she tell him what she thinks about him? She daren't say anything. He will only shout at her. "How dare you speak to me like that?" he will say.

Differences in use are not as fixed or clear cut between doesn't dare to and daren't as they are between doesn't need to and needn't, except in expressions or collocations such as:

* How dare you? > How dare you walk away when I'm talking to you?
* I dare you to… I dare you to go up to him and ask him for a date.
* I dare say… > I dare say you're pretty hungry after all that cycling.

In this last example, I dare say means I suppose.

Occasionally you will find mixed modal/ordinary verb structures, such as:

• He didn't dare complain about the quality of the food.
  
• Don't you dare! > Don't you dare throw that snowball at me!

Note that dare, like other modals, is never used in progressive form and need is not often used in progressive form:

• I was driving as fast as I dared.
  
• Are you driving into town today, Tom? Jack needs a lift.
  
• Will you be needing any help with your homework?