In situation #1, I sure as hell wouldn't run into another room, call 911 and wait for my heros to show up on white ponies. I'd do just as described. Not aiming it, not speaking - just draw and maintain eye contact. When he runs away, then I'd head for the phone.
Situation #2.....I picture a couple car lengths (what, 20 feet or so?) and closing fast. Sure I could yell for him to "STOP!!" before drawing, but he'd be down to 10 feet away by then. For some people, I'm sure that his displaying a weapon (knife, etc) would be the deciding factor and that's why I left it a mystery. Even with no weapon in his hand, if he is menacingly making a B-line right at me, I am drawing. Not aiming at him - just showing him the gun. It;s important that people key in on the word "menacingly." If he were skipping rope or playing hopscotch, things would be different....we all know a threatening look when we see it - it's instinctual. I am not a large man and would probably get brained by someone 5'11" or bigger, so to let him close in on me for a fist fight ain't in my book of options.