Can I generate payment adresses while offline?
No, you don't need to be online when generating a new receiving address, as this is done locally by your bitcoin-core. You also don't need to be online to receive funds to these addresses, as long as you protect your wallet and keep your system free from malicious software you are the owner of these addresses and you will be able to check their balance as soon as you get online and let your wallet synchronize with the network.