The Trump administration’s embrace of unproven or debunked theories about vaccines and Tylenol has left doctors fielding questions from worried parents.

A two-term Democratic governor, Ms. Mills called herself “battle tested” in an interview. But she faces a Democratic primary before she can challenge the Republican incumbent.

Ukraine’s security services said the mayor held Russian citizenship, which is forbidden, but he denied the accusation. Government opponents see it as part of a power grab.