If I understand correctly Toodledo keeps 6 months searchable history with Pro subscriptions.
?are these stored on my computer or Toodledo's server?
?Lets say that my computer gets a virus, is there a way to recover all the tasks I had open a week ago?
Toodledo is a web-based application. All of the data is on the Toodledo server and not on your computer. (Unless you are using a third-party desktop application to sync with Toodledo.)
Any viruses on your computer will not affect the Toodledo data.