A regular pentagonal pyramid is composed of five equilateral triangles and one regular pentagon. Each equilateral triangle has three angles of 60 degrees each. The regular pentagon has five internal angles of 108 degrees each.
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Normally four but there could be six if the opposite edges at the apex met at right angles.
It can, but they can also all be the same.
It will have 2 opposite equal angles of 33 degrees and 2 opposite equal angles of 147 degrees
The shape you are describing is a triangular pyramid. A triangular pyramid has a base that is a triangle and three triangular faces that meet at a single point called the apex. The base of the pyramid is a rectangle, which is a quadrilateral with four right angles. The triangular faces of the pyramid connect the vertices of the base to the apex.
Each angle of an equilateral triangle measures 60 degrees. They are all the same.