The show has started.
It means:
Show has started doing something.
For example:
I have written an essay.
It means I am the one who write.
How can the show do something by itself? How can this be correct?
So, I think the show has been started is the correct one BUT I have seen people saying and writing:
The show has started.
I am very confused. Help me understand which is correct.
Another confusing example:
The movie has started.
Why not:
The movie has been started?
You are dealing with the so-called middle-voice.
Shortly, a form of active voice is used instead of passive voice. So your observation that something does not fit was correct.
From Wikipedia:
In English there is no verb form for the middle voice, though some uses may be classified by traditional grammarians as middle voice, often resolved via a reflexive pronoun, as in "Fred shaved", which may be expanded to "Fred shaved himself" – contrast with active "Fred shaved John" or passive "John was shaved by Fred". This need not be reflexive, as in "my clothes soaked in detergent overnight". English used to have a distinct form, called the passival, which was displaced over the early 19th century by the progressive passive and is no longer used in English. In the passival, one might say "The house is building.", which may today be rendered instead as "The house is being built." Likewise "The meal is eating.", which is now "The meal is being eaten." Note that the similar "Fred is shaving" and "the clothes are soaking" remain grammatical. It is suggested that the progressive passive was popularized by the Romantic poets, and is connected with Bristol usage.
A transitive verb takes a direct object:
I threw {the ball} to Mark. ("I threw to Mark" is grammatically unacceptable)
An intransitive verb does not take an object.
I ran to Mark.
Some verbs can both transitive and intransitive and they may not have any (remaining) differences in spelling or pronunciation.
Transitive:
Please start {the car}.
Intransitive:
The show starts (at 7). ("at 7" is a prepositional phrase, not an object)
Has started is the present tense (has) perfect aspect (started [past participle]) of the intransitive or transitive.
Transitive:
He has started {the car}. Get in.
Intransitive:
The show has (already) started. Sit down.
All of your "has been" questions concern the passive voice. The passive voice is when the recipient (passive) becomes the subject (voice). It is not the default mode of communication (that would be the active voice).
The ball was thrown by me.
"How can the show do something by itself? How can this be correct?"
I think you are confusing agency (or cause) with grammar.
When I observe something as if it's performing an action, I can describe it as performing an action:
The alarm sounded.
The ball rolled down the hill.
The car ran over my foot.
The knife cut my finger.
The movie started.
Grammar doesn't care how or why something happens (or who or what ultimately causes something to happen). It only cares about what is observed to occur—or what is being described.
Whether or not a statement makes sense depends on how it's commonly used—and how much thought we give to the meaning behind it.
For instance, the movie has started is a true statement. Yes, a person did something to cause it to start—or it was on some kind of a timer (either mechanical or controlled by software) that caused it to start. But why the movie started doesn't change the fact that it did start.
It's also true that the movie has been started (by someone or something). Both statements can be made, and they would both be equally valid.
But, idiomatically, we normally just say the former. And most of the time we don't care about the agent behind the action. (Unless there is some reason to think about it.)
