The third film, tricky to be sure of what really happened?

I was wondering something yesterday, and maybe one of you can answer my question.
When the Buckbick (no idea how to write the name) is going to be killed, Hermione, Ron and Harry are in Hagrid's hut. Then Hermione "past" launches a stone at Harry's head so that they realise they have to leave the hut. They go out of the hut from the back while the "past" who were behind the pumpkins get on to the top of the "hill". Then the "past" hide in the forest, while H, R, and Harry hide behind the pumpkins and then whe fude and the others entered the hut, they go on to the top of the "hill".

My question : As the camera does not show Buckbick when it is supposed to get its head chopped, do you think that it is still alive at the end the first stage or that it has actually really been killed and the "past" is then going to come to save the bird?

The big question: did Dumbledore knew from the biginning what was going to happen, did he decide from the beginning that they were going to return in the past and save the bird?
I know it is not really clear so if you have questions
, ask me.

So I think that the time is a big circle... So I think that Buckbik has never been killed, even when Harry and cie thought he had been killed.

well actually buckbeak wasn t beheaded in both of the section...because Harry was there to save him...in the first section when we are not supposed to know that Harry and Hermione were going back in Time Harry is hit by the stone and Hermione looked in the Wood because she has seen something...so The Harry and hermione were there to save Buckbeak all the time...hope you understand

Yep so it is clear that the camera wants us to THINK it is killed but actually he is not.
Ok, understood. It's bloody well done!