Ci is used as a reference to a part of a previous sentence. See: http://www.uvm.edu/~cmazzoni/3grammatica/grammatica/ciene.html
From DL tips:
“Ci” and “ne” replace prepositional phrases. “Ci” replaces “in” or “a” and their object.
So in this case in the sentence “Non posso credere a questo” you replace “a questo” with “ci” and you get:
- non ci posso credere
- non posso crederci
(both are correct)
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".
I think it's English that is being more inconsistent here if you think about it. For example you would say "he cannot believe" not "he cannot believes". The verb "believe" is actually in the infinite form but the 'to' is just being omitted.
"The form without to is called the bare infinitive, and the form with to is called the full infinitive or to-infinitive."