you add one horizontal line to the "l" thereby making it a "t". then you add one vertical line in the form of an "l" after the "e" and, voila, you've made a "hole" into a "hotel".
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Not really, but if you have many lines it can look like a curved shape.
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The usual definition is that the lines should be straight. On "alternative geometries", other definitions may be used. For example, on a sphere, the large circles (the largest you can make, whose center is the center of the sphere) replace straight lines. Note that in this case, the normal parallel axiom is no longer valid.
Add together the lengths of all the sides that make up the boundary of the shape. These need not be straight lines.
No not just any shape that has 8 side can be called an octagon. An octagon has straight lines that make up a closed bounded shape.