Garp is seen many times before his actuall appearance as an official character. He is a marine with a dog shaped hat on all the time. He trains Coby to be a marine. But his actuall appearance was I think during the Water Seven ark where they meet Franky. Luffy is healing after the battle and Garp crashes through a wall while Luffy is sleep eating and gives him the 'punch of love' and wakes him up. He is then revealed as Luffy's grandpa.
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The cast of Garp - 2009 includes: Nadine Gharzeddine as Soraya Yannis Rappas as Yannis
He loves him like his children. XD
In manga, they met in episode 416-230. It was when the team was defeated singlehandedly by Bartolomew Kuma and they were sent in different locations. Luffy was sent to the island where Boa Hancock was the leader and became friends though Hancock have a secret love for Luffy.
Shanks loses his arm while saving a young Luffy from a Sea King. Luffy had just previously been abducted by a group of bandits, the leader of whom had taken Luffy out to sea and had been subsequently eaten by the same Sea King.