What is the shadow weave?

Where can I read more on it?

Who do I talk to about what my char will know IG?

The Shadow Weave is, from my limited understanding of it, Shar's super-secret shadow version of the weave. Evil/deluded mages faithful and loyal to Shar make a deal with her (or some divine proxy) for access to the Shadow Weave, and there are minor changes to spells based on descriptors. Shar doesn't trust many people with access or even knowledge of the Shadow Weave - possibly even from her own clergy - because Mystra would not be pleased, to put it mildly. And Shar probably doesn't have the energy and attention to spend on a high-traffic network. (Like, the Weave is hosted on a T1, and the Shadow Weave is hosted on DSL...)

I make no guarantees about the accuracy of what I've said. Edit: There's also this article over at Forgotten Realms Wiki.

Really, no PC in EfU is going to know about the Shadow weave as it is so super secret.

Roger that. Cheers.