The part you circled is the check valve. If it is only making the noise while you are pumping, then that is pretty normal for ALL air guns. It's not really normal to leak from the barrel, though it is common. It really shouldn't leak from the white trigger valve, but it will if it's even SLIGHTLY out of position.
About the barrel leak: If it doesn't pump up, seal, and HOLD pressure, then the problem is likely the glue holding the air restrictor in to the tank. This is a common failure, but requires the complicated procedure of dissection to repair.
Well, for sure the leak is coming from the barrel. I hope I can get it fixed when I attempt the Loaner mod. Sorry for sounding like a noob.