is it mandatory for a judge to wear a robe while on the bench? why?

Answer 1

It is a traditional sign of their authority in the courtroom. They are presiding and the robe sets them apart in that function.

Answer 2

It depends on the local rules. Some jurisdictions absolutely required it, others are more lax. Where I practice, judges in lower courts sometimes come on the bench in their regular clothes.

Answer 3

Yes, it's just part of tradition like those goofy wigs in England.