When may a party put to its own witness questions of the kind permitted in cross-examination by the…

Under section 157 the Court has discretion to permit such questions, so the answer is "With the Court's permission". The calling party has no right "As an unrestricted right without Court permission", the power is not barred as "Never, even with Court permission" suggests, and "On the opposite party's consent alone, without Court permission" is wrong because the adverse party's consent does not replace judicial permission; the permitted questioning also does not prevent reliance on credible parts of the testimony.