While it's true, that Aggregates represent the physical aspect of storage, Volumes are not just a partition of an aggregate, but the logical representation of storage, made accessible to end users through storage access protocols (NFS/CIFS/ISCSI/FCP/...).
The number given as 'Available Capacity' for the aggregate is space available to be given to new volumes. It is not the amount of space actually being in use by user data, since volumes might have space guarantees set ("Thick Provisioning" - as yours obviously does). Also there's a certain amount of Meta Data within an Aggregate and you might have set space aside for Data Protection purposes ('snap reserve'). Therefore the aggregate will always have more total capacity than the sum of the total capacities of the volumes - if you thick provision... That should answer your second question.
The 'Available Capacity' within a volume represents the amount of space that is available to 'end users'. Therefore if you 'Thick Provision' your volumes it is nothing unusual, that you have more space available within your volumes than there is space available for additional new volumes in the aggregate. That should answer your first question.
If you want to calculate 'Available Capacity' from a user perspective, and you have a very traditional simple-minded approach to provisioning (everything thick provisioned, no dedupe, no compression, ...), then indeed you just have to sum up the available capacities of the volumes. (Third question)... But that will be a far cry from the maximum possible capacity!
Thin Provisioning and Deduplication/Compression can be a game changer!
We ourselves for example have a 15TB volume in a 3TB aggregate (obviously thin provisioned...). It contains ~14TB of user data - it's our virtual lab environment, very high dedupe rate. There's still almost 1TB free space in the aggregate! As you can see, to calculate the 'available capacity' from a user perspective can be a bit more complicated that to just add something up.
Utilisation rates even (far) beyond 100% are not unusual on NetApp storage.
(Utilization = Amount of used logical storage / Amount of physical storage)
My recommendation: Read up on the way NetApp does storage and/or take a NetApp Course.
You might (should!) have bought training units with your NetApp kit which you can use for this...
NCI (NetApp Certified Instructor)
- FastLane Training Centers: e.g. flane.de (my home base) or fastlaneus.com