Any angle of your choice. The polygon need not be symmetric since it is not regular.
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If ll the angles of one triangle are the same as the angles of another triangle they are similar. Rotation is always allowed and mirroring often can be allowed.
One-sixth
If you rotate a 20-sided regular polygon by 360/20 degrees, the result will look the same as the original polygon. Any additional rotation will be a multiple of this number.
The answer depends on the centre of rotation. A rotation cannot be described without specifying the centre of rotation.
There are many angles inside a circle. You have inscribed angles, right angles, and central angles. These angles are formed from using chords, secants, and tangents.