. What factors shape our identities? What parts of our identities do we choose for ourselves? What parts are determined for us by others, by society, or by chance?

(1) "If we may collect the sentiments of the people of America, from their own 
most solemn declarations, they hold this truth as self-evident, that all
men are by nature free." 

Nature in this case is used talking about what comes naturally to a person. It's using it like it is their natural response to become free. 

(2) "Some are of such a nature that they cannot be surrendered."

Nature in this case is used to talk about a person's qualities. This is indicated by the words "some are of such." In this case, their nature doesn't allow them to be surrendered, or give in.