triangular pyramid
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three sided figures consist of only triangles, while a four sided figure consists of any quadrilateral, so you can draw more figures with 4 sideds than with 3
Only the square has.
No, only your brain can. Similar triangles can be used to solve some problems but not others but it is for you to work out - using your brain - whether or not similar triangles are relevant and then to figure out how they might be used.
A heart. Triangles can have more than one depending on the type.
There is no solid figure with only four edges. The smallest solid figure is the tetrahedron, made up of four triangular faces, but it has six edges.