Could you please advice how to add new Folder for a new content:
for example I would like to add a new folder for new pictures and
some sub folders. Thank You

Several ways: You can create new albums on the upload tab or on the albums tab directly. It should be pretty self explanatory. Take a look at these screenshots:
http://www.zenphoto.org/screenshots/zenphoto-admin/gallery.jpg.html
http://www.zenphoto.org/screenshots/zenphoto-admin/upload-image-jquery-multifile.jpg.html

Additionally you can also use FTP to upload folders with images or further folders to the root '/albums' folder directly.