(Caution: I am now officially making things up. Specifically, transmutations lore).
Why's a spider formed dragon still hurt by dragon slaying? Because deep down, he's still a dragon. In his heart. His soul. The cores of his being. That's beyond the scope of transmutation. Instead of changing the expression of yourself, you're changing what yourself
means. Instead of reorganization, you've talking redefinition, recreation. Once you get into that stuff you're kind of crossing into the realm of divine powers. Or at the very least crazy transcendental enlightenment metamental nonsense. And we don't even have a skill for enlightenment and/or philosophy (get Grimm working on it, maybe :p).
Why can't a spider formed dragon use his breath weapon? Cause he's got the wrong respiratory system. Why can he still use his acid bite? Cause he's still got a viable delivery system. Why can he still spit poison? Cause
spiders can still spit.
Basically, forms incorporate whatever is compatible (and/or fundamental) from the natural form of the caster, and overwrites everything else. So one caster's spider form isn't necessarily the same as another's. Statue forms reflect different body types and shapes. And in the most extreme example, a draconian's genetic heritage will drastically affect his or her dragon forms.
Now, I did make all that up, but it makes sense, and is consistent with the in game interaction of the various forms with racial and non-racial mutations.