I have another Ledger ordered so I might wait till it arrives and make sure I have a backup of the backup before I start moving anything! I know it's straight forward enough but I'm getting a little paranoid of screwing up somewhere along the line.
You don't need a second ledger to have a backup. Actually this doesn't give you more security at all.
All you need to backup is the 24-word-phrase. This phrase can be used to import your wallet into a new ledger or to import your wallet into any other
BIP39 compatible wallet.
Back to your first question:
Moving your funds from the paper wallet to your ledger makes it probably easier to be "organized" during forks.
But there is nothing wrong in leaving them on your paper wallet. You won't lose any coins and importing/splitting shouln't be a problem either.
Its completely up to you. I, personally, would store them all together on my hardware wallet.