If I calculate T and B vectors from a parametric surface, when are T and B going to be orthogonal? What are the conditions to be met for this to be true?

I don’t have the answer to your question. But the same issue comes up with grid generation. It is simply a property of the mapping; for most computational PDE’s people choose orthogonal mappings (i.e. the sperical coordinate system is orthogonal).
But your question interests me in the same way, what texture unwrappings are orthogonal? I second interest in the question!