It has two regular polygons which can be used together to tessellate a plane.
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
It is simply a shape which has two bases which are regular polygons. There is no special name for such shapes.
two polygons with sides that have all equal sides and angles
Yes, regular polygons will have all sides equal length, and all angles the same. If two polygons of the same number of sides are 'regular' then those two polygons will be similar (they may be scaled, for example).
All angle of two similar regular polygons must be equal.
Yes, the corresponding sides of two similar regular polygons must have equal lengths. This is because both the polygons are similar, which means that since they are also polygons, they must have equal lengths.
square or octagon
polygons our stuff I do not know
They are a regular pentagon and an irregular pentagon.