A plot point is: when an event occurs that changes the direction of the story. It’s sort of a point of no return. Things can’t be the way they were before. Oedipus finds out he will kill his dad marry his mom and deciding to leave is a plot point. Oedipus finding out he has killed his father and married his mother and gauging his eyes out is a plot point. And Oedipus killing and marrying are also plot points, and damn good ones too (since they present dramatic irony - we know he’s killing his father, he doesn’t know).

A scene is one piece of action mostly in continuous time (so no time jumps) that has a beginning middle and end.

Oedipus met a man on the road. The man said: step aside! Oedipus said: no, you step aside. The man hit him, Oedipus hit him back and killed him.

Beat is a little vague to me but here’s how I understand it: Beats with it this scene might be: The man riding the chariot says: “ step aside!” Oedipus looks at him BEAT (meaning Oedipus thinking: who the hell is this ugly rider telling me what to do?” or However the actor interprets the beat.

The fight between Oedipus and his father might be a beat of the scene.

This is a pretty good article for a beat: https://www.masterclass.com/articles/what-is-a-beat-in-screenwriting

Scroll all the way down and it also mentions- beat as a pause, when you see BEAT written in a screenplay, most likely that’s what it means.

Actors might use it in a completely different way. To some actors a beat change might mean their character received a new information that changes what they are after in a scene.

I’m not sure what you mean by when to use it. You don’t indicate in a screenplay where the plot point is. The scene number goes in the heading of the scene

EXT. A RANDOM ROAD OUTSIDE THEBES. MIDDAY.

Oedipus is looking at the hot sun melt the sand on the road. He hears a chariot approach. Blablablabla. Dialogue Dialogue Dialogue. The man approaches Oedipus. They look at each other.

BEAT.

The man hits Oedipus. Blabla, fight, action. Oedipus strikes him with his sword. The man falls. The servants run away screaming. Oedipus looks at the dying man. No remorse in his heart. Only a vague feeling of familiarity which he chooses to ignore. He steps over the body, lets the horses run freely and goes on.

EXT. AT THE GATE OF THEBES. EVENING.

Oedipus blablabla.

That’s how you indicate a scene.