Ci is used as a reference to a part of a previous sentence. See: http://www.uvm.edu/~cmazzoni/3grammatica/grammatica/ciene.html
It is not. "Non lo posso credere" would be acceptable. In Italian, indefinite direct and indirect objects come before the verb and after "non", or they can be attached at the end of the 2nd verb (the one in the infinitive form.
So, this could also be written as "Non posso crederlo" or "Non posso crederci".