The answer is YES. All teeth have roots. Even baby teeth have roots. As the adult tooth grows underneath, the sprout out towards the surface, and resorb the roots of the primary tooth. This is why when baby teeth fall out, all that is seen is the tooth, and no root.
This is what I used to believe teeth were. I had no idea that it was held in by a root, a root which is usually longer than the visible tooth itself! And I only found out when I learned about tooth anatomy. Most patients getting a tooth pulled are also surprised to see how big their tooth actually is when it is connected to their bloody root.
The fragment of tooth in photo 5 is what usually gets placed in the pillow.
However, if the adult tooth and the baby teeth are both in the mouth, this means there isn’t enough room for the adult tooth to take residence in the child’s mouth. Best get that checked out by someone who knows what they are looking at.