cut into 5 vertically (4 cuts) and into 4 horisontally (5 cuts) 5x4= 20 identical pieces
7
an infinite number
8
We'll say 9 cuts.
As no constraints on the shape or regularity of the resulting pieces are made, making a three by tree line grid on the pie surface would result in 16 separate pieces. Cutting the pie into regular wedges with 6 straight cuts passing through the center would result in 12 pieces.
21 cuts required to cut a cube into 504 identical pieces.
9 pieces
216
7
If you do not re-stack the pieces, then 15 cuts.
If no cut intersects any previous cuts, then you can just slice it into 14 pieces.
324
26
In one sense you cannot. The cakes would have a different number of faces which were part of the original faces. To that extent the pieces will not be identical. If such pieces are considered identical, and if the cake pieces can be stacked before cutting, then 9 cuts will suffice. Without stacking, 12 cuts are required. If the cake can be stacked and cut, and a little wastage (less than 2.5%) is pemitted, then 7 cuts will be enough.
26
7
An infinite number of ways. Cut along a line from anywhere on a side to the centre of the square. Make three more cuts, at 90, 180 and 270 degrees to the first at the centre. Each point on a side of the square will give rise to a different set of four identical pieces of the square. And there are an infinite number of points on the side of the square. So an infinite number of answers to the question.