Have you tried downloading the compatible epub2 file, instead of the epub3 file? I don't think I've used Calibre to test our ebooks on, generally we test on eink devices and tablet reading software, all of which works more or less fine. Unfortunately the state of ereading software today looks a lot like the terrible IE6/Netscape days of yore, where there are no standards and everyone does their own thing differently. It's difficult/impossible to make one file that will render well across all devices.

There is no search function because our catalog is so small. It's growing though, so maybe it's about time to add a search function too. Sort by first name is an oversight that I hope to be able to fix later this week.

Our edits don't go back to Project Gutenberg, because our final files are so different from what PG produces merging would be impossible. We also introduce typographical and spelling changes that they might not want to accept.

Yes, FBReader and other readers that use OPDS can add our catalog: https://standardebooks.org/opds/

Edit: Just tried reading the Alice compatible epub file using Calibre 2.55 on Ubuntu 16.04 and it seems to render fine. Maybe you can send a note to our mailing list and we can discuss this in more detail so I can get things fixed?