I'm new to plugin writing, but intermediate in theme making. I wonder if it is possible to write a plugin, to add addition functionality for users, who don't have admin status. Can I give them permission for upload images and so on? Can I write a plugin, what help no admin users upload and manage their images, and some personal texts?
The rules for themes and plugins are basically the same. You can make plugins and themes administrable by anyone in most respects except that non-admins can't install and uninstall plugins/themes.
For instance, you should use the if_current_user_can('do_stuff') conditional to handle permissions on operations. Also, the add_menu_page() function lets you specify what capabilities a user needs to have to be able to see it. Same as a theme.