How could Harry and his friends survive the fall without the charm?

Firstly, understand that these spells were not present in the book and were part of the movies only. In the book, the bank robbery and the cart ride go very different from what has been shown in the movie. It is not mentioned that they fell from such a great height and how Hermione saved everyone. So, this was added/changed by whoever created the movie script. Also, if you start to compare the movies with those earlier in the series, you will find a lot of inconsistencies such as that. That is mainly each movie was made after the books came out, and while other books were being written. So, something new might come up in the next book not shown in the current film.

Now, to answer your question -- in the department of mysteries, if you see that, they did not fall from a great height as had been implied in Deathly Hallows. There could be the reason they did not use a spell. Also, it could be from all the chaos that was happening. They were in a middle of a fight.

What I personally think is this -- It was the scriptwriter's idea to include the scene, and to make it more thrilling and logical, they added the fall, dramatized it, and cashed on Hermione to save everyone using a spell. Just one of the several thousand things they decided to change from the book.

While I have not seen this movie in a while, I will try my best to explain as this scene is fuzzy in my memory.

If I recall correctly, this is right before they encounter the rest of the Order in the Department of Mysteries.

One of a few things could have happened here:

• Due to the effects of the strange objects in this Department, it is possible that they stopped the fall of the group, allowing them to land safely.
• In the book, speechless spells are a thing, and are not mentioned as well in the movie, but still happen. It is also possible one of the group (possibly Hermione) used a speechless incantation of Arresto Momentum to stop the groups fall.
• The third reason is that since the Order members are awaiting Harry's group, they could've noticed the fall from a distance (assuming they didn't just Apparate into the Department) and used the spell off screen.
• It is a simple plot hole not thought out by the directors.