For example:

$A graph consisting of a vertex with three edges connecting it to three vertices in a row above it.$

$A graph consisting of four vertices arranged in a V. The left point of the V connects to the bottom corner of the V. That vertex is connected to a vertex half way up the right side of the V, which is then connected to the vertex at the right point of the V.$
This is not possible if we require the graphs to be connected. If not, we could take $C_8$ as one graph and two copies of $C_4$ as the other.
Not possible. If you have a graph with 5 vertices all of degree 4, then every vertex must be adjacent to every other vertex. This is the graph $K_5\text{.}$
This is not possible. In fact, there is not even one graph with this property (such a graph would have $5\cdot 3/2 = 7.5$ edges).