Buffy didn't die in the Angel spin-off. But since Angel Season 2 takes place the same time as Buffy Season 5, her death was announced in the Angel Season 2 final " There's No Place Like Pltz Glrb".
Yes he would though they can't be together because he would lose his soul and become angelus. But he did technically die for her in season two when she stabbed him to keep the world from being sucked...
Technically, she didn't die on Angel. She did die twice on her own show and the second time it was referenced on Angel. The first time, she was killed by the Master and given mouth-to-mouth by Xander...