Sorry to disappoint but that's untrue. Angel was brought back only because of the spin-off otherwise he would have been left in hell (at least for the time being).
And why did he get a spin-off? Because he was popular (and also because Joss was impressed by his performance in 'I only have Eyes for you'). So it's the same thing.
Nothing to do with fans. Whedon loved Elizah and the energy she brought to the set.
I've seen both versions in various places. Which, BTW, is the same with Spike - sometimes people say that he was brought back because of his popularity, and in other times people say that he was brought back because the showrunners loved James Marsters' performance (they constantly talked about how Spike made every scene he was in better).
That...doesn't even make sense.
Sure it does. Angel tortured Buffy mentally for months in season 2, and he killed and mutilated people that she loved. Logically, she may know that he wasn't at fault (because of the soul thing), but that wouldn't change her emotions - I don't think she should be able to feel love toward Angel after that. It's hard to feel love toward a face that terrorized you.
But maybe I'm just not romantic enough...
Ratings would disagree with it being a better show. When more people prefer watching reruns of earlier Seasons rather than new episodes that should have told the producers something.
Well, it made the show better FOR ME. And apparently it made the show better for Joss, too (he said that his favorite seasons are 5 & 6, and that his favorite of Buffy's boyfriends was Spike). Other people may disagree, and that's fine. It's all a matter of taste.