The Highschool DxD manga has indeed finished. It wrapped up after completing all the planned story arcs and providing a satisfying conclusion for the readers.
Well, the plot of Highschool DxD manga light novel is centered on the supernatural. Issei becomes a devil and gets involved with the devil society led by Rias. There are battles against other devils, as well as conflicts with angels and fallen angels. Each character has their own backstory and powers. For example, Rias has her own peerage which she uses in Rating Games to gain status. Issei's growth as a devil, both in terms of power and character, is a major part of the story. It's also full of comical moments, especially due to Issei's perverted nature which often gets him into trouble.
The Highschool DxD manga has gone a long way, presenting detailed plots and character developments. However, to know exactly how far it has gone, you might need to check the latest releases or related manga forums for the most up-to-date information.
The Highschool DxD manga has gone a long way, presenting exciting adventures and romantic elements. But as with any manga, its continuation and extent are subject to multiple factors like popularity and the creator's vision.