When an animagus transforms, what happens to his clothes?
(It is mashma that part of the transformation transforms the clothes into the animal; see by McGonagall she has the glasses around her eyes, as does Rita Skeeter.)
How does the transformation work without a wand? Barely any magic at all can take place without a wand. (The child wizard magic is similar (eg Lily making the flower shrivel and grow again). Voldemort can perform Legilimency without a wand, as can Snape and Dumbledore. Quirrel in Book 1 “snaps his fingers” to bind up Harry, without any mention of a wand.)