It is possible if you use the internet without using a firewall program ( you don't necessarily need to be in a chat room, just sitting there connected to the internet is enough) or download stuff without using a virus checker.
If it was your personal stuff that was wiped then it's treated as more malicious than criminal. If it was the Police National Computer or a govt. site then the boys in blue would take it very seriously indeed.
everything is possible ... firewall or not ... (see the hacker prosecution this very week) - I have a chum who is now a security consultant who did this sort of thing for fun (but real hacker don't do damage - they just leave tracks)
Instantly ...no - the prog needs to be started up somehow (at boot time or by you opening a document or whatever.
however this sort of thing requires quite a high degree of knowledge - are you worth that amount of attention?
(not many people are)