

Self hosting search engines is very hard. The scraping, indexing and storage requirements are immense. You could definitely self-host a front end (with your QoL improvements), but the back end search engines (Bing/Google/etc) will be able to track you all the same.
None that im aware of. There are webscrapers, and I guess you could just webscrape and dump the results into a postgres db and use it to index. But I’m guessing you’ll eventually want something more tuned/custom? But even if it existed, there is the discovery problem. How do you find the sites to scrape? Bing and google both let site operators submit urls, but that isn’t gonna scale to self-hosting.