Can the FBI indict someone unilaterally? Or do they only recommend their boss, the Attorney General, to take one action or the other? For instance, in 2016, the FBI recommended not to press charges against Hillary Clinton. Is it how it usually works (only recommendations with the AG having the final say)?
None of the above. A grand jury issues an indictment. It usually (universally?) does so at the recommendation of a federal prosecutor, who may decide based on a recommendation from the FBI. This is required by the 5th Amendment, which says "No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury, except in cases arising in the land or naval forces...". See this DoJ account of charging, and this broader FAQ on federal indictments.
A Grand Jury Must Indict https://youtu.be/NnbIQePbG2w Federal government to use grand juries for all felony crimes federal indictment can only be brought (or in technical terms “returned”) by a grand jury, which is a body of 16 to 23 citizens chosen from the community. The grand jury hears evidence and testimony from witnesses presented by the prosecution. It has the power to ask questions, and subpoena witnesses and documents on its own. Once the grand jury hears the evidence, it votes to indict or to not indict, based on whether there is “probable cause” to believe the defendant is guilty. A minimum of 16 grand jurors must be present to vote (a quorum), and at least 12 must vote in favor of an indictment before charges can be brought.