Maybe if I explained the anatomy of a primer it would help more people understand what is happening.
Typically the IN is angled while the out is straight.
The main thing that goes bad on them is the O-Ring dries out. Rubber or neoprene will soak up fuel, and then when it dries out, it shrinks.
When primers are brand new, the factory puts some grease around the O-ring to keep it from drying out before installation. Fuel running through them cleans that grease out, so the seal between the O-ring and the wall is now dry. Air will leak around the O-ring and out the plunger shaft.
When fuel is put back into the primer, the O-ring swells back up to seal it. First few pumps with fuel in there, the O-Ring has not swollen up yet and will pump a little bit of fuel back up the plunger shaft and onto your hands. Let it sit for 10-15 minutes and that will clear up.
The spring is there to prevent the plunger from extending while simply riding down the trail.
The check valves rarely go bad. They are basically just BB's in a tube.
A dry primer will not suck fuel into itself. You must prime the primer. I typically do this by pressurizing the gas tank and forcing fuel into the system. Carbs will fill up and stop accepting gas after about 10 seconds (with ~ 5 PSI on the fuel tank). If that still doesn't work, inject some fuel directly into the input line. Or, better yet, 2 stroke oil.
At the end of the riding season and you're putting away the machine for the summer, pump some 2-stroke oil directly into the primer. The oil is thicker than fuel and will keep the O-ring fresh. Even if the 2-stroke oil dries out, it is very tacky and leaves a residue which will keep the seal. When fuel is pumped through, the 2-stroke oil and/or any residue will be washed away.