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.
Hancock and luffy's crew and shanks
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.
The fight between Luffy and Crocodile starts from episode 122
Episode 236
episode 37 the arlong arc
It is in Episode 461, 'The Beginning of the Battle! Ace and Whitebeard's Past". Ace meets Shanks in a cave, thanking him for saving his brother Luffy.
he defeated lucci in episode 309
Hancock and luffy's crew and shanks
Vivi was met, in her guise as Baroque Works agent 'Miss Wednesday', in episode 62.
Episode 518 she gives him a boat so he can meet up with his friends.
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.
Genzo gave Luffy CPR in episode 39 and 40 also Nojiko resumed CPR on Luffy in episode 40.
it is episode 53 .. chapter 100 in manga
It has never actually happened, yet. Chronologically, the earliest we've seen of the pair is in a flashback to when Luffy first got his devil fruit powers. The two had already known each other for some time at this point. Then throughout the rest of the eps, all the way up to today, Luffy hasn't met him again. The closest was when both were at Marineford, though Luffy was unconscious and Shanks declined to see him, saying it would forcibly break Luffy's promise to him.
The fight between Luffy and Crocodile starts from episode 122
One of the four warlords, Red-Haired Shanks. He
Episode 337 "Venture Into the Devil's Sea! The Mysterious Skeleton Floating Through the Fog"