No. You do not have to answer any questions. And sometimes, police will have other people (such as alleged victims) call you on the phone to ruse you into a statement that can be used in court. So be careful speaking on the phone.
Not true. They either have enough evidence for an arrest already, want you to make a statement that could lead to arrest, or are just trying to make you feel as though you have to comply. You have the right to speak to whomever you want, and to refuse to speak to whomever you want.