Yes, and that's why I switched to Kagi
brenno
It uses activity pub, a protocol that allows servers to share content. So when you post on an instance, it became available for other instances to consume your content.
About slowness, it can be that your instance it being rate limited, or it is not powerful enough to process all its users. You can try another instance.
Activity pub documentation: https://www.w3.org/TR/activitypub/
Another option is SearXNG. It's meta search engine, which means that it aggregates other search engines like Google and Bing but without tracking or logging, because your searches are proxied using a public instance, that will mix your search with the ones from other people.
And about default search engine, don't know what you're talking about, both chrome and Firefox allows this, in mobile and desktop.
Papers please. Having fun so far doing the story