You should be able to download books via Safari on the standard Web UI. When you try and download a book then you should be offered an "Open With" option for the file type - if it is an epub this will include iBooks. Not sure why you do not seem to be getting this. I tried your link and got the same results so I am confused.
Another option is the OPDS view (which I prefer) but this needs an OPDS aware app running under iOS. If you use an OPDS aware reader such as MegaReader/QuicKreader then you can use this directly. An alternative is to use the free "ebook Search" app (by the author of MegaReader/QuickReader) that can interface to an OPDS catalog and after downloading give you the "Open With" style dialog that was mentioned above for passing the book to your prefered reader program. I tested your OPDS link with the eBook Search app and it saw the library and seemed to think there was an epub avaiable that it could pass to iBooks. However it failed to load into iBooks
It sounds to me as if there might be a problem with your download links? What OS are you using - I have seen issues when there is a case mismatch between the filenames on disk and the filenames that Calibre thinks should be there.
P.S. I am not sure if any of the books in your library are copyright? If so you should not post a link to you library in a public forum.
Another possibility if you have access to a web server is to use the
calibre2opds software to generate a static catalog instead of using the Calibre Content Server. This is what I normally do for my own library as I can host the Web Server on a NAS which means I do not have to be continually running Calibre.