I think she was really happy, not because emma the one who save her but because henry asked emma to save him, her face just lit up when she know the truth
she seem doesn't really care when emma and mary got sucked into hatter's hat, but I think she will try to save emma because this time henry ask regina to save emma
I think she was più surprised in that scene and maybe feeling a little bit guilty, does she cared? emma still the women who took henry away and snow is her mortal enemy, so she probably doesn't really care if they're gone But she care about henry and she will do anything for him, even if this means saving her mortal enemy, she will do it, this probably the first step of her redemption,
One giorno they may 'respect' each other in a way that they'll both do anything to keep Henry safe, happy etc. It's kinda hard to imagine straight away though! I think it will gradually 'develop' into a 'loving mothers for son bond??'