You are wrong.
Unless you use a brainwallet passphrase that was randomly generated with very high entropy, brainwallets tend not to be the "safest way" to keep bitcoins. Furthermore, memory loss and confusion can result from a variety of situations (age, illness, physical blow to the head, etc). In which case a brainwallet becomes completely useless.
I you really want a brainwallet, then yes you could use bitaddress to do so.
The URL won't work while offline. You need to download it.
Paper wallets and brainwallets are generally intended for secure long term storage of bitcoins you don't need to spend on a regular basis. When you want to send the bitcoins somewhere, you'll have to import the private key somewhere to sign the transaction. If you do this on an online computer, then you've immediately lost the benefits of offline storage. You could use Armory to handle signing the transaction offline if you like.
Yes. At that time you should consider xxx no longer as secure as an "offline wallet" (such as a brain wallet or paper wallet). If you still want the security of an offline wallet, you will need to create a new offline wallet and send any remaining balance to the new wallet.