No calendar subscriptions showing up on iCloud.com
This is likely because iCloud.com only has iCloud calendars. Chances are all the rest of your calendars are not iCloud. Honestly, I wouldn't see it as a bug, but something that they haven't added into the online portal. If you click the Settings icon and select Preferences in iCloud.com/#calendar it will not give you an option to add outside calendars.
They will still show up on your phone because it is tied in with your email. If you go to the email account that you are subscribed with, you should see Calendars set to "On".