Their first fight is over episodes 435 and 436, their second fight is 449 and 450.
episode 37 the arlong arc
The fight between Luffy and Crocodile starts from episode 122
Episode 236
In the anime they haven't yet. But my prediction is that if they fight eventually Luffy will own him. Mainly because he can hit logia users with haki now.
I'm presuming your refering to the fight between Luffy and Usopp back on Franky's island WaterSeven/Aqua Lagoona. Well they were fighting over whether they should leave their ship, Merry, behind as it had become broken beyond repair after their visit to the Sky Island. Usopp wants to save and repair the Merry, but Luffy see's sense and knows it's safer to leave the Merry behind. Usopp challenges Luffy to a dwell, which Zoro forsees and prevents the others from getting involved and stopping them. Luffy, enevitably, wins.
episode 37 the arlong arc
Luffy and the rest of the crew arrive at Cocoyashi village around episode 31-32. But the famous march to aronlg park, which is what i think your looking for, takes place around episode 37.
The fight between Luffy and Crocodile starts from episode 122
he defeated lucci in episode 309
Luffy fight gecko in episode 371 or 372
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
Luffy is terrible with a sword, the only times he has used them is once against Arlong to display how he relies on his comrades to cover his weaknesses, and secondly while on Thriller Bark, when he inherits the shadow of a marine swordsmen.
Episode 236
Episode 408.
Luffy ends up on Amazon Lily, the island of women, in episode 408.
it is in episode 3.