If I've bought my EOS tokens through Bitfinex and now hold on my offline wallet, do I still have to claim them?
Note - if I enter the EOS address into etherscan.io, it finds both my Ethereum and EOS balance. Does that mean they are linked and I don't need to do anything?
You should create your profile in the EOS system which must be connected to your Ethereum wallet. The sharing of tokens would be provided in the EOS system as you understand yet. You can use different wallets which support Ethereum coins.