Efficiency. Polish.
There are many reasons why "need not" is preferable to "do not need to."
Most importantly, the shorter construction is more efficient. (1) It is more readily understood, neurologically. (2) Therefore, it is stylistically preferred. (3) Aesthetically, the iambic meter is more pleasing to the English-speaker's ear. Notice that the rhythm of "need not" matches Shakespeare's iambic meter, a little like a pleasant gallop. Following are some examples of iambic meter:
Robert Frost:
Whose woods these are, I think I know ...
Shakespeare:
If music be the food of love, play on ...
In contrast to this rolling rhythm, the mono-syllabic "do not need to" sounds emphatic, angry, every word a punch.
For your second question, regarding the use of "be" versus "to be," please provide context. I'll be glad to help!