It's hard to find competitive eating results for anything other than the Nathan's hotdog contest from before 2000 but everything I can find points to the pickle thing being true. He verifiably came in 3rd in the 1994 Nathan's hot dog contest, and emceed the 2002 pickle contest as a "former champion." The story about the deli guy telling him to compete is almost certainly made up though, since it changes every time he tells it.

The mafia hit also seems real, Gotti was tried 4 times on it and it was pretty much accepted during those that he had ordered the hit but was able to convince enough jurors that he had left the mafia before 1999 making the 2004 trial past the statute of limitation.

Also this lmao: