Since the question is unfinished, I'll assume the most obvious completion: "planes."
Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
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No, intersecting lines form four pairs of supplementary angles
Yes. If two intersecting lines form the angles A, B, C and D (in rotational order) then AB, BC, CD and DA are pairs of supplementary angles.
Four.
Four pairs, which intersect at the four vertices!
They would be called intersecting lines.Intersecting lines form Vertically Opposite Angles. Each pair of opposite angles (sharing only a vertex) is congruent. Each of the four pairs of adjacent (sharing a side) angles forms a straight angle (they add to 180o).