First, I'm assuming this is the abbreviation of Article Number. How is this field intended to be used?
It's just for reference information. It can be used internally to reference a payment line item, but it's not really used for anything beyond that.
Second, how are the individual Art. Num. values generated for each item on an invoice? Is this also customizable?
They're generated internally and cannot be customized. They're formatted as follows.
TYPEPURCHASEID-USERID-PLANID
The types are as follows
Subscription = S
Merchandise = M
Donation = D
So you might have the following for example.
M1-10-1
These are then stored with payment items in _cbsubs_payment_items.