until you release that due to needing an account, all your search queries are tied to your account and even if they claim not to, it would be trivial for Kagi to associate all of them with you.
and we don't have the code of their servers, we know nothing of how they handle this critical information, other than their "trust me bro".
(and even if they are not directly associating this information, if they store some kind of logs, it would probably be trivial for any third party that gets access to their servers to make the association. an again, we know nothing about their procedures)
I don't think so. They have commercial agreements with Microsoft that forces them to not block their trackers, so who knows what else they are obliged to by contract
https://www.bleepingcomputer.com/news/security/duckduckgo-browser-allows-microsoft-trackers-due-to-search-agreement/