1) Everyone is seeing the first issue you mention.
Supposedly, on the HD, there is no separate partition for Shop Content and sideloaded content (like on Color and Tablet).
So ALL 13 GB of storage should be available for things you buy from B&N. However, everyone is seeing something like 9GB or 9.7 GB.
My assumption is that B&N kept apart 3 GB for OS stuff and in-built apps. Then it set aside 13 GB for stuff we buy or sideload.
1) They are reading the wrong value and showing just 9GB - space used.
2) There is a bug and it only allows 9GB for stuff you buy from the shop.
I suspect it's the former.
2) STorage Management. Another user had the same issue. I don't - I get the accurate number of apps.
However, other users have just 28 to 35 apps but show 96 apps downloaded. There is an option to actually see the list of apps. In your list of apps do you see 24 or 99. That'll clear up that it's just a small error.