Episode 44, which is also her second appearance...sadly we viewers do not hear her first actual words. She has already been talking for a while as Jaken states. I kind of wish we could have...I wonder what she said? <3 <3
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Episode 80: "Sesshomaru and the Abducted Rin"
*Mt Hakurei Episode 111
Rin first appears in episode 35 after she finds Sesshoumaru. I don't recall all the episodes, but my favorites are episode 80 and 81 (Rin is kidnapped and Sesshoumaru saves her), episode 96 (Jaken Falls Ill. Sesshoumaru saves Rin from falling off a cliff after she tries to find a cure for the poison that the Saimyosho injected into Jaken) and 162 (my ultimate favorite where Rin is kidnapped again and Sesshoumaru is attacked by a pack of monks. He battles them and then gives Rin a second choice; whether she would like to continue following him or stay with humans). She appears in Lot's more. These are just my favorites. Oh yes, she appears in the last two episodes (166 and 167).
Whenever you first meet Sesshomaru in the 1st Season Jaken has been with Sesshomaru even before the series started. You do get to see a flashback Jaken has. He tells Rin about his first encounter with Lord Sesshomaru and why he is so loyal in Season 3 Episode 79: Jaken's Plan to Steal Tetsusaiga
Not yet, Rin, Sesshoumaru, and Kohaku have only gone to Hell during the manga. In the final act (japanese) they go to hell in episode 9.