Can the police enter my house?
Only with a warrant or “exigent” circumstances such as: they are chasing you, they get an emergency call that someone is being beaten or shot, a fire emergency.
You have a heightened expectation of privacy in your home. Therefore the police must get a search warrant before they can enter your home, or have a real good reason to tell the judge.
What is a home?
The law protects persons: not places. So what is in your mind is determinative.
Your home can be anywhere you feel like home: at a hotel room, as an overnight guest, in your room in a rooming house. It is always an open issue and an arguable question: like a snail who carries his home on his back: think home.