Creating a mesh on top/inside of a mesh In the linked video at 6:40, how did the author create a face on top of the figure? How do you create a new mesh/plane on top/inside of an existing one?

https://www.youtube.com/watch?v=kfebPwr0gx4

Also,
the faces on the mesh in the image are not flat because the edges are bent in places where there are no vertices. How do I make flat faces?
Create a new object (plane), get into Edit mode, and use the Snap option (and Type > Face) so that the vertices of this new object stick to the other object behind. Also, enable the Project Individual Elements option (so that when you extrude, both the vertices stick to the other object).