The carousels on the home page show the courses in date order, meaning the newest course will always be first.
You can also check for new courses on the My Courses and Learning Plans page, which will show you all courses without splitting them up by learning type, which the carousels on your home page does. You can also see all courses here, whereas the carousels will only show you the first 24 courses. Make sure the 'Newest to Oldest' sorting type is selected at the top right of the page.
If you are subscribe to the full corporate library, any new courses will appear with a black 'New' identifier in the top right corner. This identifier will stay until you have started the course.
No email alerts are sent when a new course is launched.