Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle.
Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from a vertex to the opposite side and is perpendicular with that opposite side, it can only occur if it is outside the triangle. Look at the triangle in related links.
If you look at the vertex on the top, the only way to draw the altitude would be to draw outside the triangle.
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yes
The triangle's altitude is 8.7 (8.66025) cm.
No. The altitude is smaller.
With an altitude of 10 units, this triangle's sides each measure 11.55 (11.54701) units.
If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.