Well they've (people above) answered your questions already but I'm just gonna add:
•Taniyama Kisho of the band Granrodeo. The band performed most of Kuroko no Basuke OP and Taniyama also voices Himuro Tatsuya from the series
• Suzuki Tatsuhisa of OldCodex, the band performed most of the ED of Kuroko no Basuke too while voicing Takao Kazunari. They also performed OPs for Free!! and Tatsuhisa voices Makoto.
•Ono Kensho who voices Kuroko Tetsuya sung 1 or 2 OP for the series too. He has released his own albums too.
•Osaka Ryouta, Shimazaki Nobunaga, Hanae Natsuki, Yoshitsugu Matsuoka, Aoi Shouta, Sakurai Takahiro and other seiyuu of Diamond no ace did a number of EDs for the series.
•Teru of GLAY, he's not a seiyuu but made a cameo at an episode of Diamond no Ace season 2 and another in an OVA. Glay performed a lot of EDs for the series.
•Tomatsu Haruka who voices Yuuki Asuka performed a couple of song (OP and ED) for Sword Art Online
•Sakamoto Maaya voices Tomoyo in Tsubasa Chronicle also sings ending song "Loop". She had released several albums and a number of her singles got featured in animes as opening and ending songs weather she got casted or not.
•Morikubo Showtaro who voices a lot of famous characters and a well known Singer, gave life to a game character Mega Man X back in 2000 and sings the the theme song of Rockman X6.
•Even Takeuchi Junko (Naruto's VA) did a cover of one of Naruto Shippuden OP Distance originally by Long Shot Party.
There are still others, but I think this list is enough. The band Flow doesn't have any members who do voice acting. I think so does the Ali Project. As for the others you've mentioned, I am not familiar with them.
As for the seiyuus singing the OPs and Eds, I don't think you have to be part of the cast for a certain anime to sing its OP or Ed or You have to sing its OP or ED to get a role in the show. I'm taking a wild guess that it all depends on the director and the sponsors. You know for marketing purposes. They're the ones who decide who gets casted after all.