NEEDN'T & DON'T NEED TO. What's the difference between them?

http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv317.shtml
  

There is also a difference in use when these verbs are used to describe present situations. We can use both needn't and don't need to to give permission to someone not to do something in the immediate future. We can also use need as a noun here:

You don't need to water the garden this evening. It's going to rain tonight. 

You needn't water the garden this evening. It's going to rain tonight. 

There's no need to water the garden this evening. It's going to rain tonight. 

You don't need to shout. It's a good line. I can hear you perfectly. 

You needn't shout. It's a good line. I can hear you perfectly.                                      

There's no need to shout. It's a good line. I can hear you perfectly.

 

However, when we are talking about general necessity, we normally use don't need to:

You don't need to pay for medical care in National Health Service hospitals.

You don't need to be rich to get into this golf club. You just need a handicap.

NEEDN'T HAVE & DIDN'T NEED TO. What's the difference between them?

 Both these forms are used to talk about past events, but there is sometimes a difference in use. When we say that someone needn't have done something, it means that they did it, but it was not necessary. Didn't need to is also sometimes used in this way:

You needn't have washed the dishes. I would've put them in the dishwasher. 
You didn't need to wash the dishes. I would've put them in the dishwasher. 
I didn't need to prepare all that food. They phoned to say they wouldn't be coming. 
I needn't have prepared all that food. They phoned to say they wouldn't be coming.

 But we also use didn't need to to say that something was not necessary under circumstances where it was not done:

The sun came out so we didn't need to take any rainwear on the trip.

We had plenty of petrol in the tank so I didn't need to fill up.

We didn't need to wait for long for them. They arrived just after us.