It's been several times that I catch him/her doing this, I don't know what it means, and I was wondering if some of you knows?!

That's an odd video - your bird seems to be displaying a combination of male and female mating behavior. The singing and dancing back and forth is male behavior, but the flat-backed posture is similar to the position that a hen takes when she wants a male to mate with her.

He/she is not the one whose singing, h/s does like a peep sound ,
The one on the following photo is the singing one,
They don't preen each other, they live in the same cage, don't fight, but the one on the video reject hims.
So, you think it's a she?

The bird in the video is certainly acting like a girl. If she can back up far enough to touch her vent to the perch she might start pleasuring herself. I was half expecting to see that happen in the video.

The face looks more like a male but looks can be deceiving. I can't see the markings very well but he/she looks like pearl or pearl pied. Pearl hens have a lot more yellow in the face than other mutations do, and with pied you can't tell the gender by looking at the face color.

I have read and keep researching about hormonal behavior, but so far, this is the only thing he/she does. And it's being randomly
Also, he/she is 9 months, is it possible to start hormonal ?

Thanks for your responses!
Really appreciated

It is possible for them to start acting hormonal at this young. I've seen them do it at younger.

Can you take a picture of the bird in he video? It looks like a Pearl, and if it is, that might explain why the face seems slightly bright. Pearl hens have slightly brighter faces than other mutations (Lutino and pied being an exception).

Since your bird is 9 months, it probably went through the juvenile molt already. It if really is a Pearl, then that would mean it's female. Males start to lose their pearls after a juvenile molt. Can you take a picture of its back, as well as its front, so we can see the wings?

Thanks!
Hope this will help

Definitely a pearl but I don't see any pied. I do see a new tail feather coming in with the same coloring as before. Looks like a hen to me!

Great!
So, looking at the other bird, do you think I got lucky and I have a male?

The picture is so dark that it's hard to tell much. I don't see adult male coloring but it looks like small areas of the face might be starting to change from grey to yellow. But the singing sounds very male so I think he's a boy.