I'm a really beginner, I have no client on my computer. I puchased bicoin and store them in my wallet at blockchain.info, and I have downloaded the "backup file" named "wallet.aes.json". My concern is if someday the website of blockchain.info shuts down, can I get my bitcoins by importing the backup file into a client software? I also have my "key" which is a long code that looks like an bitcoin address, and my understanding is that the backup file also only consist of my address and that key. Thanks!
You can import this backup to Multibit, and you are good to go, even if blockchain.info is dead. (To be honest, this is my setup as well). Remember to keep your secret safe and use 2FA.
As long as you have recent backups (meaning you have to keep making backups everytime you do a transaction) and know the passphrase you should be able to access your coins should blockchain.info go down. But it is not recommended to use blockchain.info for storing large amounts i.e. amounts that you can't afford to loose. Blockchain.info wallets have a tendency to get hacked. I recommend installing electrum and sending your coins over to your electrum wallet.