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If an external intersection is considered an intersection
If not, but a tangent at a boundary point is considered an intersection.
No. It refers to an intersection within the segment, of course.
It's not possible. Why? Because if we draw several connecting segments through a line, and then try to connect the beginning of the first segment and the end of the last, we will have two options, regardless of the segments themselves:
1. The connection of the segments lies on one side of the original line (and does not intersect it)
2. The connection of the segments intersects the line, but also intersects other segments.
I'm sorry, you are wrong.
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Ничто не возникает из ничего и ничто не пропадает бесследно.
Если где-то чего-то убудет, то в другом месте добавится.

(Закон сохранения).