The only way I know to set tags on pictures, is to use the admin album page, and per album, we could see the images and here we could setup tags for pictures... But this is quite painful.

Is there another way to set tags to picture more easily ?

I was wondering for example if a plugin could allow us, directly from the site, when we are logged in, per image to see all the availables tags as check box that we could check...
Tx

Your best way is to set the "keywords" metadata in the images themselves. Second best would be to use the bulk actions on the image tab. (Or the individual image tag settings also on the image tab if you really mean image by image.)

These actions do show you all the tags available (and even allow you to add tags if you want) so I do not understand the question of showing all the available tags.

If you want to set tags (or actually do any other editing) from the front-end image page, then that is not available. It is not available because it is a huge security risk as the front end does not have the level of security protections (and thus the overhead) that the back-end (admin pages) supplies.