Okay, you have what sounds like a DSA STG58A kitgun. The flash hider looking thing is DSA's BATF approved copy of the original Austrian STOLL FH/Grenade launcher device except it doesn't have the prongs. So it's really just a barrel weight.
The lower receiver is an Austrian STG 58 with the markings and selector. Several components are required for a select fire FAL.
1. Searcut upper receiver
2. Searcut ejector block
3. Auto safety sear
4. Auto bolt carrier (underside of bolt carrier has lugs, one longer than the other)
5. Auto selector
Your rifle doesn't have 1,2, and 3. DSA should've put a drop of weld on the selector groove to prevent pulling the trigger in the auto position.
Anyway, without the safety sear, the theory is that if the hammer is allowed to follow the bolt carrier rather than being caught by the primary sear, there isn't enough energy to set off the primer. Essentially it's slam fire. The reason it fired twice in semi and closed on a live round is because the hammer followed the carrier and wasn't reset or caught by the sear. Fortunately, it's in battery when this happens. Did you get this rifle straight from DSA? Who said it was a pre-ban? I'd verify with DSA on that one.
My suggestion is to [b]NOT[/b] fire it in the Dauerfeuer position. Put a drop of weld in the selector slot or get a semi-only selector. It is not legal to convert this rifle to select fire mode.
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Also, with ammo loaded with "softer" primers or primers not seated deep enough, there might be enough energy in the hammer to set it off.