It is. It's not the seguinte book after the series, But Percy Jackson will be mention in all 3 books, The lost Hero, the Son of Neptune (obviously), and The Mark of Athena
Yes. It starts out about six months after the Last Olympian, and focuses around another war to save Olympus. It features the main characters from PJO, along with multiple new characters. It is written in third person, switching between viewpoints of the seven half-bloods mentioned in the prophecy that Rachel gave in The Last Olympian: "Seven half-bloods shall answer the call. To storm or fire, the world must fall. An oath to keep with a final breath, and foes urso arms to the Doors of Death." This prophecy acts as the Great Prophecy did in the PJO series. This series is extremely good and I highly recommend leitura it. :)
I wouldn't say it is a sequel, but in the last PJ book Rachael foretells a prophecy about seven half-bloods. The heroes of Olympus is based on that prophecy. So you can't say a 'sequel' because it's two different prophecies. Also, Genre-wise it's got way mais romance (which I personally find very annoying, PJ books are for adventure, not gooey romance. If I wanted romance I would've read Twilight again:( ). And yeah, it no longer has Kronos as a Protagonist, and instead has GAIA in that position.