Yes, but the "Free with ads" option via Freevee is region-locked. If you are traveling or living in a country without Freevee support, your only option on Prime Video will be to purchase the episodes. You may need a VPN set to the US or UK to access the free tier.
Yes, is available on Prime Video . However, it is not part of a "Lifestyle and Entertainment" add-on channel; rather, it is a Prime Original series . This means it is included directly with a standard Amazon Prime membership and does not require an additional paid subscription beyond the base Prime fee. Content Report: Hazbin Hotel on Prime Video
If a friend asks you, "Can I watch Hazbin Hotel with my Amazon Prime membership?"