there are actually few more statutes but I'll start with this one -
wanna try to answer my question?
"when approaching a suspicious person, do you think it is possible that it can end badly?"
3 fallacies in your argument -
1. mall cops are easily identifiable with badges/insignia and uniforms. are you?
2. armed mall cops? NJ-NY are basically USA Capital of Malls

and I've never seen armed mall cops but either way - if they're armed, they're most likely have been authorized and trained by law enforcement agencies and/or are either former or off-duty police officers.
3. you are very confused. Rights to self-defense and Rights to self-defense with deadly force are 2 two completely different things and both has completely different legal criteria.
any further question?