On the Harry Potter Wiki, it states that:
Unlike Animagi, Metamorphmagi can take a wide variety of forms, changing sex and age, potentially looking like anyone at all, or even just changing a part of their appearances, such as the shape of their noses. Animagi also transform at will, but only into one animal form which is determined by their inner traits. It is never revealed if Metamorphmagi can take the full form of an animal, however it is very likely to be true if practiced hard enough and with the right skills
Also, a Metamorphmagus is born, not made; it is not a skill that can be learned. There also seems to be a degree of heritability, as both Nymphadora Tonks and her son, Teddy Lupin, were Metamorphmagi, although both of Tonks' parents, Andromeda and Ted, were not. The ability presents very early in life, as Teddy Lupin's hair changed colour when he was a newborn infant, as did his mother's.
Not sure how true this is, but most other Google results for 'Metamorphmagus' say very little on the topic. Fact is, we really don't see much of Tonks in the books, and while they may not use her abilities much in the Order, we've never seen how she uses it as an Auror and the only thing that's ever really said about it is in the beginning of the 5th book. It's not a topic covered much in the books so really, its open to speculation. If she could only change her appearance and not her shape, she wouldn't be able to change the shape of her nose. She probably just simplified her description for Harry. If she can do a pig nose, why not a hand into a paw? If she can change her hair colour, style and length, why not grow a beard? Can she change her skin into another texture or substance? Could she be like a chameleon and blend in with brick, or bark, or leather? Can her hair turn into feathers or leaves? We know very little about metamorphmagi in canon. As stated earlier, it really is open to speculation and, most importantly, up to your imagination. I doubt, however, that she could completely turn into an inanimate object. Animal, perhaps (probably mammal? Something with at least a passing similarity to humans, like a cat or a dog. I doubt she could turn into a goldfish or an ant). Plant, maybe appearance and shape (like a tree, with bark skin and leaf hair and make her body look like a tree shape) but I doubt she could turn into a daisy. A vase or a chair? Highly unlikely, in my opinion.
Another interesting thing to consider is an idea I got from some fanfictions. The idea is that there are various degrees of ability, some Metamorphmagi can only change hair colour, others hair and nail length, right up to those who can completely change age (even turn into a child), shape, sex, race etc.
But we'll probably never really know. Has anyone ever asked J.K.Rowling?