Say a succubus from Savage Species chooses to look like a country's queen as her alternate form. But she also wants to use her demonic claws and wings. Can she just take the queen's appearance as her alternate form, then assume a "hybrid" appearance (the queen, but with claws; or the queen, but with wings) or would doing so require taking three separate alternate forms?
No; the alternate form ability always indicates specific forms that a creature can swap between.
A creature with this special quality has the ability to assume one or more specific alternate forms.
Lycanthropes simply have three forms, the base creature’s original form, an animal form, and a hybrid between the two. They aren’t the only creatures with more than two alternate forms, and they’re not even the only creatures with an alternate form set as a “hybrid” between the other, but it’s not a general thing about alternate form in general that allows it. (And, for that matter, the hybrid form is just another specific form, not any ability to mix and match—a lycanthrope couldn’t choose to be halfway between hybrid and human, for example.)
And just to confirm, yes, the succubus loses her claws and wings:
The creature loses the natural weapons, natural armor, and movement modes of its original form,