is it possible to use the notion of organization within the tickets and not only on projects?

As of today, no
With screen customization plugin, yes.

Is it possible to sort the projects (and tickets) with the organization notion ?
on the top of tickets and projects like the type,id and name?

Whjen screen is customized, filter on organization will be possible.
To have extra field on direct filter, some develomement is required.
Please contact us if you want an estimate of corresponding development