Drawing and Justifications
I agree with most of the logic in these posts: Don't draw your weapon until your life is in immediate danger. Otherwise you could be in worse trouble. There are many options avaliable to you - if they are practical - take them instead - retreat, evasion, HTH combat. But if you must....
Here are my inputs on the 2 scenarios:
1) At home vs BG - Well first I wouldn't look through window, I would turn off my interior lighting and turn off exterior lighting and try my peephole. If he threatens, I will retreat from doorway take cover, and tell him I am armed. Never breaking eye contact with entry points. (At this point weapon would be drawn and pointed at doorway. No shooting through the door or anything like that - too dangerous. Would call 911 if phone was next to me. But if I had to go to next room to get it, no way. Keep entranceway(s) covered.
Turning interior lights off definitely gives you an advantage over BG as you know the layout of your home. Also as the outside light is on, he would be perfectly silhouetted target as he broke in.
2) Parking lot vs BG - No way I draw here. I would stop, look at avenues of retreat, and / or additional threats (peripheral vision) , and not break eye contact with BG. Verbal warning if he continues to approach. Act accordingly as scenario unfolds. No way do I draw unless he has a visible weapon.
But if I were to draw - then I would use weapon (unless he made a hasty retreat as the weapon was being displayed.)