A: Not usually!
Invisible Cosmic Zebras are INVISIBLE so nobody really knows what they look like. The art project is a way for you to dream up and imagine what your Invisible Cosmic Zebra might look like. Some people might imagine that their Invisible Cosmic Zebra looks like a real zebra, but most will imagine that it looks more like a cosmic creature. No two Invisible Cosmic Zebras will look the same.
Invisible Cosmic Zebras are COSMIC because they usually feel "alien" to those who have to take care of them. For example, when you're diagnosed with an invisible illness it doesn't feel like "you." It feels like it's from another world because it doesn't live by the same set of rules you're used to living by. And others might not have any idea what you're talking about when you try to explain it to them.
And Invisible Cosmic Zebras are ZEBRAS to represent their big (invisible) size and the fact that they take up a huge amount of (mental) space in our lives.
An Invisible Cosmic Zebra is a fun and loving metaphor for an invisible illness that you have to take care of every day, possibly for the rest of your life.