Work is underway on an API to do all of this. Nick and Scott are hacking on it about three feet to my right just now. The days of scraping are numbered.
YCombinator doesn't endorse Algolia's HN API in any public way, to my knowledge. This makes it just regular third-party API—reliable, convenient, better than scraping, but hardly ‘official’. (Yes, I'm being pedantic.)
It seems to in the sense that Algolia powers the HN Search at the bottom of every window, and they are co-branded on those search pages. Also, https://hn.algolia.com/api
I agree, but it's good marketing. It associates the act of searching with the hostname 'algolia', which seems to be in their interest (being that their tagline is "Hosted cloud search as a service | AlgoliaSearch").
[1] https://hn.algolia.io/api