On a sphere, the lines of latitude and lines of longitude will always meet at right-angles.
I agree that they won't on a plane.
They do on both, obviously you are misunderstanding the FE model.
Draw 2 circles, do it.
Then from the center point, draw 2 lines radiating outwards, doesn't matter where
The angle where the line meets any circle will be 90
oEvery point on a circle is at 90
o to a line from the center, that's how circles work.
What you have done is drawn a perpendicular bisector of a tangent.