I would install an antivirus on Linux. I know that this system hasn't problem with virus, but I would be sure that my friends don't receive infected files from me.
Could you suggest me a software easy to use and automatic, such as Norton for Win?
There isn't anything similar to Norton (I think the win version is rubbish anyway, but thats just a personal opinion) for Linux. You could try AVG for Linux or something like Clamav.
you're better off using something like chkrootkit.
make sure to turn off any services you're not using too! (and/or firewall them)
I ever heard rookit hunter. Btw, chkrootkit is a anti-rootkit and also an anti-virus? and what about clamAV? is it also an anti-rootkit?