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In our world a triangle can have three right angles on a sphere: consider the triangle formed by the Equator, Longitude 0o and Longitude 90o.
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Yes. A right triangle is a triangle where one angle is a right angle. If two out of three angles are right angles, then it's an isosceles triangle. If all three angles are right angles, then it is an equilateral triangle.
Three.
No, an equilateral triangle as three 60 degree angles.
The most right angles a triangle can possibly have is 1. Any more than that, and it has to be a quadrilateral.
All three interior angles of a spherical triangle may be right angles.