You don't need to just blindly trust, there are ToS and privacy statements. My TL;DR is that Google doesn't use logs outside of service health (eg vs DDoS).
I don't know. I think not everything a large company does necessarily immediately pays for itself. Also, Google overall benefits when people use the web more.
Nothing or Google depending on how you want to think about it. Google needed this service for themselves, as the default fallback DNS for their devices, their domain registrar, for GCP and it made sense to just let the public use it too for some good PR.
