Can I use Quetzals ability without a barrier icebreaker on the desk? (i thought for interacting with an ice and break its subroutines you first need to break the ices strength)
The exact rule is that, in order for an icebreaker to interact with a piece of ice, that icebreaker must at least match the ice's strength.
As for miss green-hair, she can, once per turn, break a barrier subroutine. (Additional bonus. Import a piece of E3 Implants from criminals and break the rest of that ice's subroutines for a penny each!)