I agree with daybreak_fairy, if Gold really wants the curse broken and the only way to do it is for Emma to die he’d just kill her and get it over with. So there must either be some other way or something he needs from Emma that she needs to stay alive for.
As for Regina, I took that as a forshadowing too. When she said it my head just went “that can be arranged” xP The tree does seem to have some connection to her power but I doubt she’d die if it were cut down, if she were physically connected to it we’d have seen a bigger reaction when Emma cut the branch off it.