Legal Question in Criminal Law in North Carolina

Sure, if you let them. They can even enter if you don't let them however, any incriminating evidence they find would most likely be inadmissable in Court. Also, there are other circumstances where law enforcement can enter a house without a warrent or permission. For example, if an officer can see something through a window of the house that would give him or her probable cause. The officer may enter without a warrent or permission.

Sometimes. It depends on the circumstances. The officer can enter if she gets the permission of someone who is (or reasonably appears to be) authorized to let her in. She can also enter without a warrant if she reasonably believes that somebody inside is in imminent danger or under a variety of other exigent circumstances.