Can private keys remain offline for their entire life?
Yes, all three assumptions are correct. You can with some effort keep your private keys offline for their entire life.

A description of how to sign transactions offline is found here: How to sign a transaction using only an offline computer?



Adding a bit of detail on Assumption 3 along the lines of Tim S.'s comment: A computer that is offline would obviously not get updates from the network, so it would also not know which transaction outputs are available for spending. This could be mitigated by importing the blockchain data to the offline computer (for example with the bootstrap.dat). 

However, it would be much easier to create a two wallet setup, where one online wallet knows only the addresses, and the offline wallet has the private keys. You then create the transaction on the online wallet, which has the transactional information and sign it on the offline wallet. That's what is described in the above linked question as well.

Update in 2017: The creation of a transaction on the online device and signing on the offline device is essentially what hardware wallets such as Trezor do.