1. How are the core values of American democracy incorporated into the Declaration?
Through the fundemental beliefs, which are... Life, Liberty, The Pursuit of Happiness, Common Good, Justice, Equality, Diversity, Truth, Popular Sovereignty, and Patriotism.
2. What responsibilities does the government have to honoring these core values?
They must fulfill them.

What responsibilities do individual citizens have to preserve these core values?
They need to obey the laws the government have set before us.
3. How might some or all of these core values be important to the preservation of a free and independent press?
The laws have to be obeyed or they must press harder.
4. Identify the core values of American constitutional democracy that allow private citizens to collect, edit and further distribute information to others and how the values help drive these actions.
Just by obeying them. That would help drive them. And also the law being the law would help inforce the laws.
5. What responsibilities do producers of information have to these core values and their fellow citizens when distributing information?
Using the core values to their maximum