When are you under arrest?

At what point is a person under arrest when having a conversation with a police officer or deputy sheriff? Do the words "You are under arrest" have to be spoken?

Let's say you are walking on a public street. Say, in the middle of the night. You're an adult. An officer hails you and says, "Come over here." Add in here that you are homeless and that you are known to the police in that town (and other towns).

Do you have to walk over to him? Is it enough to stop and wait for him to approach you? Are you under arrest at that point? Perhaps many would say not, although your freedom to leave is probably restricted somewhat by his direction/order/comment/command.

Then he asks what you are doing - why are you walking around in the middle of the night? Since we enjoy freedom of movement in the United States, do you have to give a reason? It is not unlawful to walk on a public sidewalk in the middle of the night.

Then he wants to search you. Let's say you are female, and you tell him that he can pat you down for weapons; that's all. After that, he wants to look in (search) your purse (not just for weapons), and you refuse the search. So he searches your purse, anyway. Is that legal?

Then he wants to look in your backpack, and you refuse permission. So he looks, anyway, and finds a computer, which he accuses you of stealing and takes into his possession. Can he look through your notebooks and copy entries from your notebook, without your permission?

You are handcuffed and transported to the police station, where you are read the Miranda rights and sign a statement that they have been read to you.

Are you under arrest at that point?

You explain why the computer is in your possession, and it is not reported as stolen.

Then you are told that you can leave. You are not charged with any crime. But they won't return the computer, and they won't issue an evidence receipt for it. And what about the handcuffing and trip to the P.D.?

Is this an "Ooops, we made a mistake" situation? And then what happens?