After all these not so serious stories about bar kapara I wanted to find some serious facts about him.
(a) Who was bar kapara?
(b) was he related to rebbi in any way?
(c) Was he also a tana?
(d) what does his name "kapara" mean?
(e) Could he be related to R' Elazar HaKapar?
(a) The Seder Hadoros says that his name was actually Shimon (others say it was Aba). He wrote Mishnas Bar Kapara (some say he also wrote the Tosefta).
(b) He does not mention that he was related to Rebbi.
(c) The Chida writes (in his commentary on Seder ha'Doros) that Bar Kapara had the Halachah of a Tana.
(d) + (e) The Chida (see "Rebbi Elazar Ben ha'Kapar" there, which the Chida changes to "Rebbi Elazar ha'Kapar") indeed quotes an opinion that Rebbi Elazar ha'Kapar was Bar Kapara's father, and that the word "ha'Kapar" and "Kapara" refer to the city Kapar. [However, the Chida argues on this.]
Bar Kapara had many Talmidim who quote him in various places throughout Shas, most notable among them Rebbi Yochanan and Rebbi Yehoshua Ben Levi.
All the best,