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The distance around a figure is called the "perimeter", unless the figure is a circle - in that case, it is called the "circumference".
If you are talking about a perfect circle, it has wan infinite number if lines of symmetry. If you are talking about and actual lower case o, then the answer is two.
You draw a circle around a circle.
Yes the distance around a circle is its circumference
Both. "Case sensitive" means that upper case and lower case characters are treated as different characters.