It is confusing, I know but you'll get the hang of it. Law isn't the easiest thing to understand which is why groups like BASC will paraphrase things and post things on their websites for 'normal' people to follow.
YES. You are allowed to shoot on your permission, unsupervised. However you are not allowed carry a rifle outside, the boundaries of your permission/home, unless you're supervised by someone over 21.
I'll try and make it a little simpler with this visual aid...
The white areas are your permission and the areas you can shoot unsupervised. Please note that if you are