Alright, first I'll hit PU's questions, since his is the easiest:
There are 2 types of Beeline. The way you described it is for the smaller diameter with the Vectran core. The one in the pictures is the larger diameter and the core is polyester...it's Yalex to be exact. In this rope, the cover DOES add to the strength, and thus should be spliced like a typical polyester double braid so that you can take advantage of the strength of the cover AND the core.
Now as to the herniating you're seeing here. If this was in my bag and I noticed it in the morning, I'd still climb on it, but at lunch I'd call who ever made it for me and tell them what happened and that you'd like it replaced for free- and I'm sure they'd have no prob doing it. The cover is there to protect the core, and it can't do that if the core is popping out...also, if the strength is in the core AND the cover, how can the cover be pulling its fair share of the load if the core is herniating and there is slack in the cover.
I say replace, but make sure doing so doesn't cost you any more money.
Also, maybe try the smaller diameter Beeline. It's smaller AND stronger.
love
nick