Season 1 "Missing" is the episode I think you're refering to.
In the episode called 'Driven' (4x11)
He doesn't. Tony does, however, contract the pneumonic plague in the 23rd episode of season two.
It was season 3 but am not sure of which episode.
3x08 - Under Covers
pneumonic plague
Requiem
5x01 Bury Your Dead.
Sub rosa. Season 1 episode 7
Boxed In Season 2
They are going to go into the details of Tony's family in season 7, apparently Robert Wagner is going to play Tony's dad on the 150th episode of NCIS.
In Kill Ari Part 1, when she comes to the NCIS office to meet Gibbs, she meets Tony first. Then, she tells him about his schooling, childhood etc
Tony Dinozzo joined NCIS right from the beginning. He is one of the 3 characters (with Gibbs and Abby) to have appeared in every episode of NCIS that has aired till date