You should always protect everything, however iPhones and iPads have no security software designed for them as Apple doesn't deem it necessary, yet.
and home products here: http://home.mcafee.com/Store/Store9.aspx? Note that the only protection for i-products is family protection which is not antivirus/firewall.
At least password protect your phone if it is a Smartphone and I assume it is.
Is this a laptop you are connecting via your phone?
Yes, it is a dell laptop connectet to the Nokia 5800.
Is it possible to get spyware on the "Modem" (=phone)?
Not really unless you are in the habit of downloading stuff directly to the phone at other times. That would be best investigated on Nokia support forums I guess. I doubt it is in danger when acting purely as a modem.