Rectangle
It depends on how you cut it. It might be a frustrum, it might be a (somewhat differently shaped) pyramid, or it might be a wedge.
Quarter each side.
A square
You ether cut it in half or fourths or eighths(do you get the idea?)
If you were to cut a cube in half along any plane passing through its center, you would get two equal halves of a cube. Each half would still have the shape of a cube with the same dimensions, just split into two separate pieces. The resulting solid figures would be two smaller cubes.
Dome
If you cut a rectangle in half you wouldn't get a solid figure at all, since a rectangle is a plane figure. If you made a straight line cut you would get either a triangle or a quadrilateral of some variety depending on exactly how the cut was made.
Another cylinder
A rectangular prism or a cuboid.
No. Each piece of the cube would have the same density.
Another cylinder if you dissect it horizontally. In other cases, the name is unknown.
It would be a wooden cube that has been cut in half and painted red.
It would be a rectangular prism.
You would cut off a corner.
triangle
you cut it into regular solids then figure out those then add them together