You may be thinking of Unreal. (OGRE, Irrlicht, and Delta are also open source.) Aurora is the old Bioware proprietary engine (from the NWN days), which CDPR did rework extensively for the original Witcher.
Aurora Engine is not open source. There is an effort to rewrite it from scratch, but it's far from ready. It's called Xoreos project. Feel free to contact the developers and offer any help if you are interested.
Not exactly. It's some mixed ownership, since they licensed it from Bioware and added their own modifications. So in order to open it up, probably they'd need Bioware's permission as well. I wouldn't mind more opened old engines of course. Some companies do it willingly (like Id Software for example).