Vampire Academy → Frostbite → Shadow Kiss → Blood Promise → Spirit Bound → Last Sacrifice (main series, 6 books). Then Bloodlines through Silver Shadows and The Ruby Circle (the Bloodlines spinoff, 6 books, following Sydney Sage). The spinoff requires the main series first.
Yes — Bloodlines (6 books) is a direct continuation of the Vampire Academy world, following Sydney Sage (introduced in Vampire Academy). The events of the main series feed directly into the spinoff. Read the main series first.
Yes — Peacock aired a Vampire Academy TV series in 2022, adapted from the first books. It was cancelled after one season. The 2014 film adaptation covered the first novel.