I've got a Datasucker. Can I use its ability "Hosted virus counter: Rezzed piece of ice currently being encountered has -1 strength until the end of the encounter" even if I do not have any icebreaker with strength equal or greater than ice's currently encountered?
There's no restriction on using the ability aside from what's printed; you must be encountering a rezzed piece of ice. Datasucker is not an icebreaker, so the strength of the ice doesn't affect the ability. There are reasons to do this, such as Parasite