Carlos Nieto

There's a little inconsistency here:
In episode 13, season 1, he's born in 1977.
In episode 9, season 5, he's born on November 5th, 1975.

Paramedic at the 55 precinct firehouse.

Adam 55-3

Monte Parker (most often)
Kim Zambrano
Alex Taylor
Eugene
Levine

Becoming a doctor up to season 4, episode 17, then being a paramedic becomes his chosen profession.

Carlos is afraid of heights.

In season 1, episode 14, Carlos meets Vangie (she was in an accident, and Doc and Carlos were the ones on the scene) and dates her for a while. She is mentally unstable and he soon tries to break it off. She then tells him, she's pregnant. He offers her his help for an abortion, but she refuses. After a suicide attempt on her part, and quite a few rows between the two, she finally tells him that he doesn't have to worry about it anymore. Carlos ignores what she means by that, and we are left as ignorant as him on the matter. The story is picked up again in season 3 with Kylie.

Inconsistency concerning Vangie: in season 1, her last name is Evans. In season 3, her sister and Kylie's last name is Samstron or something like that (I didn't manage to hear it right). Shouldn't they be named Evans as well ?

Season 3, episodes 16, 17 and 19: to his shock, he learns that he is the father of Kylie. He dated her mother Vangie a couple of years back, and now that she died in a bike accident, he ends up with the kid.

Though he completly falls for his daughter, he decides to give up Kylie for adoption since he cannot give her a real family to grow up in. He choses the Kenny family and asks them to be able to stay in contact with his daughter.

In season 5, episode 8, he learns that Kylie is sick. She has idiopathic aplastic anemia and needs a bone marrow transplant. Her best bet is to find a biological donor. However, as Carlos puts it, she is the daughter of a "one-sibling psycho and a foster care reject who has no family", hence complicating the whole biological donor business a great deal. Fortunately, things are going change in the following episodes concerning Carlos and his lack of family...

Apart from Kylie, none really. Carlos is a foster child. But in season 5, episode 9, Carlos tries to know who his biological family is in order to help Kylie. She needs a bone marrow transplant that he can't give her. He goes to see a woman he used to live with, and learns that his father was killed in a hit-and-run and that he was found holding his hand.

Then in the following episodes, Carlos is contacted by a man who claims to be his older brother. He is a match for Kylie and so we understand he is really Carlos's brother. His name is Christian and he's a chief prosecutor from Hawaii. He's been looking for Carlos and his father for 25 years. Apparently the father had run off with Carlos after a bad divorce custody decision. Carlos's name used to be Adam (which is funny because it happens to be the name of his bus, and also the name of the actor who plays his brother, Adam Beach. The writers are having fun...).

Christian tells Carlos that their mother never stopped thinking about him until the day she died, and celebrated all his birthdays while praying that wherever he was, he was with a family.

there's another little inconsistency here:
In season 1, episode 8, Carlos says he had 6 foster homes.
In season 4, episode 19, Carlos says that he was in 7 different foster homes before he was 10 - which suggests he had more than that.

This is Ms. Lucinda Harding who used to be one of his foster moms.

The most important person for him next to Kylie is probably Monte Parker, alias Doc. My guess would be that he is kind of a father figure to Carlos. Then would come his roommate Ty Davis.

Ty Davis (since season 2).

A cockatoo acquired in season 2, episode 1, "The Lost".

S1E14: 32 Bullets and a Broken Heart
S1E15: Officer Involved
S1E16: Nature or Nuture?
S1E19: Spring Forward, Fall Back
S1E20: A Thousand Points of Light
S1E21: Just Another Night at the Opera

S2E17: The Self-Importance of Being Carlos

S3E11: Old Dogs New Tricks
S3E16: Thicker Than Water
S3E17: Falling
S3E19: The Greater Good

S4E11: Second Chances
S4E12: Castles of Sand
S4E13: Snow Blind
S4E17: Letting Go
S4E19: Everybody Lies

S5E08: Fury
S5E09: A Ticket Grows in Brooklyn
S5E10: The Spirit
S5E14: Blessed and Bewildered
S5E15: No More, Forever