This is for anyone who knows about Harry Potter. Recently I've been watching the Prisoner of Azkaban and here is the problem, I'm confused about the whole time travel thing. When we first see Harry, Ron and Hermione go off to Hagrids Hut about the whole thing with Buckbeak the hippogriffs execution and bla bla bla, you know that point where two stones are thrown through Hagrids window and one of them hits Harry? Well apparently that was Hermione who had gone back in time with Harry to try and rescue Buckbeak and Sirius Black, but the confusing part is, how come you can't see Harry and Hermione having gone back in time to these course of events whereas after we see them in the hospital wing we
Actually see them go back in time? Plus I'm also confused about the lake scene where Harry and Sirius are facing the dementors. We can sort of see the other Harry casting a patronus
From the other side of the lake but no Hermione. And then at that same point in the course of the events when we actually see Harry and Hermione go back in time we Hermione standing next to a tree as Harry casts the patronus

I'm not sure what you mean by "see" them go back in time. In the hospital wing scene, the director has chosen to simulate the act of time travel with a visual effect. In other scenes he has chosen not to show that same effect. This is purely a choice on the part of the director. I would assume he showed it during the hospital scene because it was the first time the fact of Hermoine's use of the charm was revealed. But further use of the effect was unnecessary (and time consuming).

In the initial lake scene we are not supposed to know who is casting the patronus that rescued Harry and Sirius. So it would not do for the director to show that Hermoine was standing nearby. In the later scene where it was revealed that it was Harry saving himself, we know that Hermoine was with him.

Time travel can be a paradox. Since it is a matter of fiction and no one knows what would actually happen, there are a number of things that can be done with it. Its simply up to the writer and (in the case of a movie) the director has to how to portray things to the audience.

My understanding it after the first effect, it was deemed not needed, and I would expect as in a lot of the film, it was left on the cutting room floor ( guess they don't really "cut" anymore) but I am told that a film has a lot of editing to make it fit time requirements or for things that seem to slow action down.

It was as noted, merely the producers and directors choices.