A square
The cross-section of a cube can vary depending on how it is cut. If sliced parallel to one of its faces, the cross-section will be a square. If cut diagonally, the cross-section can be a rectangle or a more complex polygon, depending on the angle and position of the cut.
Infinitely many.
Yes it can.
It will be the same shape as a square
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
No, a cube cannot have an octagonal cross-section.
A square.
Infinitely many.
Yes it can.
Rectangle
Yes, but not a regular one.
It will be the same shape as a square
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
Cube, Cuboid. Any prism with a quadrilateral cross section
Along any edge
You would cut off a corner.
equilateral, isosceles, and scalene.