#3 It's incorrect to say "we are not a democratic republic," - those aren’t mutually exclusive. The U.S. is a constitutional republic and a representative democracy—so calling it a democratic republic is also accurate. There, you've been corrected by a dope.
I've learned that whenever you say "Democracy," some dope corrects you to "Democratic Republic". Now I've learned that when you say "Democratic Republic," some dope will correct you to "Constitutional Republic." Now I wonder what the dopes will correct you to when you say "Constitutional Republic."