Yes. The two points will be the same when it is a regular triangle (all 3 sides are the same length, all three angles are 60 degrees)
The incenter of a triangle is the point at which the 3 medians (lines from the vertex to the middle of the side opposite the vertex) of the triangle intersect. Per it's definition, the incenter cannot ever fall outside the triangle. On the other hand, the orthocenter (intersection of the altitudes) can. It does so whenever the triangle is obtuse.
never
Yes. Medians always intersect in a single point, called the centroid, or geocenter.
no
No
No.
It doesn't ever fall outside of a triangle.
No two sides of a triangle can ever be parallel.
Only planes, boats and people. That's the whole point, if nothing disappeared nobody would have ever heard of it.
No
No not ever because they both have different properties
Yes, it can.