Answer to your main question is Yes, vent line open all the time, otherwise the pump would be sucking on a vacuum, which would bring everything to a halt pretty quick. The Perry pump does operate by suction by the way, not by pressurizing the tank like some other systems.

I've had good luck with Perry pumps, solved a few difficult installations for me.

I tend to prefer the 'bypass' plumbing arrangement. This has a tee installed between pump output and fuel inlet to carburetor, and results in excess fuel pressure being diverted back to the tank, where it displaces air which either goes out the vent or equalizes the volume being drawn by the pump. In any event, it provides very stable fuel pressure or head at the carb inlet, no matter what the model's attitude or G-forces (within reason, anyway).

Good idea to run the vent line above the tank, then exit to atmosphere at a point on bottom of plane, behind the tank. This way no fuel drains out as the plane goes through a loop or other maneuvers. Also a good idea to put a fuel filter in the vent line, to keep crap from being sucked into the tank through the vent line.

I've been in long arguments that have never been won concerning whether a running engine with pump operating can ever leak fuel out the vent line. I do what I've seen other good flyers do, works for them, works for me.