In addition to YaCy and the varieties of Searx (both of which perform better for me than any of the commercial search engines), it’s not even out of the question to do this yourself, if you’re willing to start with the most recent Common Crawl dump and do some spidering in between releases. I don’t recommend it, unless you want to learn for yourself why search engines often give such miserable results, but it’s possible.

However, that’s the issue, here. Can you self-host a search engine? Sure, if you want to maintain the storage to back it. That depends on how deep your pockets go…

Probably, though I don’t know their architecture well enough to say. The discussion that I saw referred specifically to PDF.js, which I believe is what the browsers use, though.

It’s not as clean a solution as they’d like it to be, but for another option, Jellyfin hosts media including books. When I say “not as clean,” I mean that you can stream video and music from the server, but it has you download books to read on another device. Last I heard, they were looking to integrate at least a PDF viewer into the interface, though.