Mac – Difference in encrypting a sparse bundle for Time Machine before or after mounting the drive

With option 1 you are encrypting the files, not the drive. Option 2 encrypts the whole drive.

To answer your first question about the keychain and whether you should encrypt backups: the passwords in your keychain are already encrypted, that's why you always have to type a password (by default your login password) to show stored passwords. So there's no immediate need to encrypt.

Of course, you could add Time Machine encryption to provide a further layer of security. This is possible starting with OS X Lion and Mountain Lion (from http://support.apple.com/kb/ht1427):

OS X Lion and Mountain Lion let you encrypt the Time Machine backup external drive using FileVault 2.

FileVault2 also uses your login password, though. So if the bad guys are able to guess or crack that password, they will have also access to your keychain information. Choosing different passwords for login and for accessing your keychain would protect the keychain passwords in such an event.

Either way, use strong passwords, password quality is of foremost importance to protect your data.

EDIT:

The OP asked in a comment how to set different passwords for login and keychain. Here is how:

• Open Utilities>Keychain Access.

• Right click each keychain and select 'Change Password for Keychain XYZ':

  

If you prefer to use your current password as keychain password and change your login password, log in using another account and change your account's password from System Preferences>Users & Groups. That will only change your login password, not your keychain password.