Yes, #3 is possible. As you suspected, it needs additional context.
Imagine that you are watching a newsreel from 1940. There is a news story made by the people of a small town somewhere in the United States. As it begins, the narrator says "A new school is built in our city." The rest of the news story is in the simple past tense, describing the events that made up the building of the school: the young family who wrote a letter to the mayor, the bond levy to raise the money, the hiring of the architect, the hiring of the construction company, etc. The story ends with children arriving at the school for its first day of operation.
The first sentence was a summary of the whole story, which also set the approximate time limits of the story. People often write in the present tense to describe a past or future event when they're summarizing events or establishing the scope of a more-detailed description. In ordinary speech, you would not use the present tense even if you were talking about the action or situation right now. If you wanted to say that the building of the school is in progress now, you'd say "A new school is being built". If you wanted to say that the building of the school is now complete, you'd say "A new school has been built." By using the simple present tense (which is somewhat unusual in English) to describe something that takes a long time, you are momentarily "stepping out of time", "stretching" the present tense to hold the full duration of the building of the school. Doing that at the beginning of a news story suggests that you will present the details momentarily. And when you do, you'll go back to using tenses in the ordinary way.
A well-known example of the same construction is the title of the movie A Star is Born. (The link goes to several movies and many songs by that name.) The title is in the present tense in order to promise that the movie tells the story of someone going to Hollywood and becoming a star, from beginning to end.
The reason for using the passive voice, of course, is only that schools don't build themselves (at least not in English). An active-voice summary of a news story might go "A communist recants and a publisher turns a profit." However, I think you'll find that this "scope-establishing" present tense tends to use the passive voice more often than ordinary sentences. (I don't know what grammarians call the "scope-establishing" or "summarizing" usage, and I recommend not finding out.)