a plane triangle is a normal triangle, like the isosceles, right angled, equilateral and scalene triangle.
No, never in plane geometry.
an example of solving a right triangle
A right angle triangle is a plane figure not a 3d one.
Scalene, right triangle.
A right angle is a plane figure and cannot have a volume.
It can be because it depends on the triangle's angles. For example, if the triangle has 2 equal sides and a right angle it could be a isosceles and a right triangle.
Not a plane triangle. With a triangle on a convex surface (eg on the surface of a sphere), the answer is Yes.
Any triangle can have a maximum of one right angle. Most right triangles are scalene triangles. The only non-scalene right triangle is a 45° - 45° - 90° isosceles right triangle. It is not possible to have an equilateral right triangle in plane geometry. A scalene triangle does not have to have a right angle, but it can have one.
A triangle has no right angles when it is not a right angle triangle as for example as in the case of an equilateral triangle that has 3 equal 60 degree angles.
Yes, if you are willing to go beyond standard plane geometry. For example, a triangle can have two right angles in addition to a third angle on the surface of a sphere. No, if you must stick to regular secondary school plane geometry.
Not necessarily. It is a plane shape which could be horizontal.