What angels and fallen angels were named in the Bible and what are they responsible for? I've also heard of works of theologians on that matter, can someone provide some references?
There are only two angels mentioned by name in Scripture:
Other Angels appear in the OT (One to Manoah in Judges to announce the birth of Samson, three to Abraham in Genesis), but they are unnamed.
An angel has only one job, as implied by the name - they deliver messages.
When they are not doing this job, they are usually in the presence of the Lord, praising him and announcing his glory (Isaiah 6, Revelation)
Debatedly, the only fallen angel is Lucifier in Isaiah 14 - the "Star of Morning" who is the Devil.
One could also describe "Legion" as a demon in Luke 5 (at Genesseret), but that isn't a proper name, rather a collection of Demons.
@Affable Geek's right, but doesn't mention the Archangel Raphael as his tradition doesn't consider the book of Tobit scripture.
Since Catholics and Orthodox include this book, he's also one of the angels named in the Bible. His name means God Heals and he's the one who took Tobias on his journey and helped him heal his father's blindness. He's actually pretty awesome.
Also, in Catholic tradition (and other traditions), it was two angels who visited Abraham and Sarah, along with God.