Does a wolf's howling ability affect their chance to get approved if we choose to howl at a spirit ancestor?

No

Is it like a random generator for picking the wolf that gets to appeal to the ancestor, and only their own Spirituality counts? Sorry if that doesn't make sense. As in, my alpha female has maxed out Spirituality specifically for this purpose, but she rarely gets chosen, and all the other wolves that do get chosen hardly ever appeal.

When exploring and you come across a Ancestor, a random wolf in your current explore team will perform Howl, Bow or Growl. Your wolves' Spirituality CP effects if you get Approved or Dissaproved. The lower the CP, the lower chance of getting Approvals. I've also found 'Bow' to be the most successful option :)