Special Counsel Jack Smith is accustomed to trying war crime and corruption cases, but come Friday and Monday he will find himself the subject of a hurricane of hearings that could upend his prosecutions of President Trump.

Judge Aileen Cannon, who is presiding over Mr. Smith’s Mar-a-Lago case, will convene a session on Friday devoted to the question of whether the special counsel has been constitutionally appointed. The judge, who has been less sympathetic to Mr. Smith’s case than her counterpart overseeing the January 6 case at Washington, will hear not only from the government and Trump’s team, but also from amicus curiae, non-parties to the case who have been granted the rare opportunity to argue orally.