It’s not very obvious I’m afraid, but you can see the size of the original files for all selected images in the Download menu tool-tip:
The webclient will struggle to generate .zip files on-demand for large amounts of data. I’m surprised if it even works well for a whole ‘page’ of images. One option is for you to create a zip manually, with (for example) all the images for a Project. You could attach this zip file to the Project as a File Annotation (and could also link this same annotation to the Datasets or Images within the Project, without adding to the data on disk). This would allow users to download without having to generate a zip on the fly.
This manual approach might not scale well if you are making a lot of data public, and you may find that the webclient still doesn’t handle downloading of very large Files very well, but it’s worth trying to see how it works for you.
For downloading larger amounts of data as scale, OMERO is probably not the right tool for the job. For the IDR, we use Aspera www.ibm.com/products/aspera.
If you have another tool for handling downloads, it could be possible to configure webclient’s Open-with… menu to direct users to a download URL for a particular Project etc, or simply add a download URL to the description of a Project or Dataset.
Hope that helps,