Does a divorce legally occur by the questioner's statement to the judge: "I said to her: You are divorced," when he did not say it to his wife, or by his uttering it a year later? And is he obligated to inform his divorced wife of that?

It is sufficient to go to the judge to issue the divorce document with the intention of effecting the divorce, for the divorce takes place as soon as the document is issued, because you authorized the judge to write the divorce and you intended to effect it. Consequently, uttering the divorce thereafter was not obligatory upon you, nor are you required to inform the woman of it, as the divorce took place since the document was issued by the judge.