I don't know the answers to all that. Also there is a shadow weave, that shadow magic uses instead of the regular weave.

Other Gods, particularly Bane, Cyric and Talos were jealous of Mystra because of the power she wielded as god of magic, but they were not subservient to her. Also just because she tends the weave does not necessaroily mean they couldn't use it. Let's remember too it is past tense because she is dead now so the weave is I guess drifting about on its own.