Explain how the Declaration of Independence preserved individual rights and formed a strong and long lasting union.

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed

With these statements in the opening portion of the Declaration of Independence, the colonists describe the importance of individual liberty...

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed

With these statements in the opening portion of the Declaration of Independence, the colonists describe the importance of individual liberty and the rights of the governed.  Thomas Jefferson, the author of the Declaration of Independence, would state that when political leaders do not provide for these individual freedoms, the citizens have the duty and right to call for a new government.  The colonists had repeatedly petitioned England to reform their practices toward the colonists, the demands were ignored.  This is the crux of Jefferson's argument for dissolution with England.  The individual and collective liberties that governments were meant to provide were not being met.

As for the unity of the nation, the Declaration of Independence was also an important step.  The thirteen colonies, to that point in time, were very different from one another.  They had different cultures, commercial interests, and histories.  The Declaration of Independence acted as a statement of shared concern.  The grievances listed in the document were shared by all of the colonies.  Consider the following passage:

That these United Colonies are, and of Right ought to be Free and Independent States; that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved;

The language of that statement is clear:  the colonies are now to be united in the cause of creating an independent political entity in the New World.