1. The OS should be safe enough from any kernel space attacks. Not so
very much on user-space. For online banking and internet shopping, make
sure you make your transactions through "valid" https and known
certificate authority. Then, you might be secure. Else, you might be
hijacked.
2. I always recommend you install antivirus (clamav,
avg) no matter what. Dont trust linux just so that it is linux. If
compromised, your attacker is certainly not a script kiddie noob.