Thanks for your interest.
1/ In Navier-Strokes euations, pressure is defined up to a constant. At the outlet we fix this constant. So it is a reference pressure. Taking the computed pressure distripution you can add any constant pressure you want. So a negative value is fine and still physical.
2/ The paper refers to a different example. There we fixed the mass flow by fixing the velocity. If you want do that in the mentioned example you may set velocity boundary conditions at the two outflows and a pressure condition at the inflow.