I am looking for a possibility to add a description to a photo during upload (for members + admin)

Afterwards it should be shown at the same place as "Photo information" (EXIF)
I am using theme "Garland"
Is this possible?
Thanks in Advance!

You can add a description after uploading. You can add it via meta data so it is read when the image is upload and the meta data read (given the related meta field is enabled).

where can i find the meta data? And how can I enable?

In fact ‘that is not what I mean...
When admin edits an album there is a tab where you can add a text description to the photo.
How can i give a member the possibility to do this aswell WITHOUT admin rights?

where can i find the meta data? And how can I enable?
Options > Image

How can i give a member the possibility to do this aswell WITHOUT admin rights?

The member does not require "admin rights" to edit photos but he requires edit rights to the image respectively album the image belongs to:
https://www.zenphoto.org/news/an-overview-of-zenphoto-users/

I tried different possibilities...
When I give him right to attach a description to a photo during upload, a normal member can delete the album ???

Yes, edit rights/management rights include that. If you trust that member to upload you should also trust it to be able to delete the image. You can limit the rights to a specific top level album incl. its subalbums.