As of version 1.12.5 of the Ingress Scanner app, we can answer these three questions as follows:
- There is a limit of 2000 inventory items; this would limit your number of portal keys along with other items.
- When you're at this limit, or if you upgraded while above this limit, your ability to hack is blocked, meaning presumably, that doesn't happen.
- It is very clearly possible to hold duplicates of keys, they are shown in your inventory with the title addendum "(n)" where n is the number of copies you own. When you scroll through the keys to make a link, each copy is it's own item card shown grouped with its like portal keys.
It's further worth pointing out that now when you hack a portal it is no longer necessary to not be holding that portal's key in order to receive a key, or a copy of the key for your inventory. E.G. without managing your inventory in any special way, you should slowly find yourself acquiring 2 or more keys for the same portal.
This version's server side changes have also made it far less likely that you'll get a key at all; I had to hack a portal I live almost on top of 20 times over two days to get a single key for it. I have yet to get the keys for 4 portals around me that were added days ago after I submitted them.