OP
Melissa - Porno Graffitti
Ready Steady Go - L'Arc-en-Ciel
Undo - Cool Joke
Rewrite - ASIAN KUNG-FU GENERATION

ED
Kesenai Tsumi - Nana Kitade
Tobira no Mukou e - YeLLOW Generation
Motherland - Crystal Kay
I Will - Sowelu

Insert
Brat'ya - Anastasia Golovina, Veronika Golovina, BEPA choir

Movie
Link - L'Arc-en-Ciel
Lost Heaven - L'Arc-en-Ciel
Kelas (Let's Dance) - Tayo Awosusi

Game
Kokoro no Hana - Motoko (Game 1)
Emotionally - Saori Yamada (Game 1)
Wishing - Naoko Mori (Game 2)
Kanashimi no Kizu - Nana Kitade (Game 3)

Character Songs

Ed
Asu he no Basho - Romi Paku
Returnable Memories - Romi Paku
Hagane no Kokoro - Romi Paku

Al
Ano Yume no Mukou e - Rie Kugimiya
Boku wa Koko ni Iru - Rie Kugimiya
Trance to Homunculus - Michiru Oshima

Roy
Tsuki No Uragawa - Toru Ohkawa
Shounen yo, Shinjiru Nakama yo - Toru Ohkawa
Ame no Hi wa Noo Sankyuu - Toru Ohkawa, Michiko Neya

Hughes
So....e Kyou mo Sekai wa - Keiji Fujiwara
Angel Heart - Keiji Fujiwara
Papa to Asobou - Keiji Fujiwara, Mayumi Yoshida

Winry
BOY FRIENDS! - Megumi Toyoguchi
Renai Sankousho ~Love reference book~ - Megumi Toyoguchi, Naomi Wakabayashi
Gindokei - Megumi Toyoguchi

Compilation
Last Meeting - Romi Paku, Rie Kugimiya, Toru Ohkawa, Keiji Fujiwara, Megumi Toyoguchi
Good! - Romi Paku, Rie Kugimiya, Toru Ohkawa, Keiji Fujiwara, Megumi Toyoguchi

2nd Series

OP
Again - Yui

ED
Uso - Sid

----------------------

If I'm missing any please post here and I'll add them to the list.

Am I stupid or...
What is this "Insert", a game?
The singers names are Russian and the title means "Brothers" if I translate it from Russian... hmm...

Insert songs are ones that are inserted into the anime. It wasn't used as an OP or ED, nor is it a vocal, so it is an insert, because it's not a BGM, and is used sometime during the episode between the OP and ED. Or something like that.

Ah, okay, thank you ^^)