The Lady in the Bottle - S1-E1
Question: What language is Jeannie speaking at first and how do they get around the three wish rule?
Answer: Regarding the three wishes, there was never any set-in-stone rule or belief. This appears to originate from "The Ridiculous Wishes" or "The Three Ridiculous Wishes" that is a French literary fairy tale written by Charles Perrault and was published in 1697. It sort of set the standard for genie rules that later appeared in other folk tales and then in movies and TV shows. Like vampire lore, common details can be changed by any author to suit their story.
Answer: She's speaking Persian. And there was never a 3 wish rule. When Tony freed her, he became her master, and she'd do anything for him (i.e. grant his every wish).
Answer: As noted elsewhere here Jeannie is speaking Farsi.