you may need different tools for the different use cases.
A cool one for being able to view multiple desktops as once is:
It's an opensource project. Used for classrooms but seems that it'll do well on your first bullet point.
We used to use a product called LanSchool which can probably accomplish the viewing of the system, but not really sure on the security requests. You may want to look into some of the Guidance Software products, they own EnCase and Tableau duplicators.
EDIT: Guidance is now "OpenText Software"
Sounds like you are looking more towards the forensic side of things rather than a monitoring/collaboration viewpoint.
Thank you for your reply.
I looked precisely on an Open Source app like this one :
If it's not possible to find an free one, we can you different softs, but is it possible to have in add a freeware that do the screenshots and also video capture ?
Thanks a lot guys !