Can the private members of a class be accessed without using any public function??

Answer 1

No you cannot. Thats the whole point of the permission levels. Even friend functions that are allowed to access/manipulate private class variables [publicly] are technically 'public' functions you're creating to do so.
I do imagine though, with some 'trickery' you could use some virtual functions & templates, mess around with some pointers & structs to hack into the private scope somehow.
Maybe even try to use pointer manipulation of an object's memory allocation that you know are certain sizes.
Basically I think it's possible but not with any conventional use.

Answer 2

no, to use private it must be accessed into public

Answer 3

Yes, if you use the "friend" keyword you can access private members outside of the class.

More details and examples:
http://en.cppreference.com/w/cpp/language/friend