4/5. Viconia choosing to send several of her cloister on a suicide mission, including the one person she has spent years grooming to be Shar's chosen is... an interesting choice, especially as she apparently has no idea what the artefact is even used for but believes it can be used against the Absolute.
The way I interpreted this is by separating Shar's and Viconia's motivations. Shar does not care about the prism, or the absolute. She might even indirectly benefit from their plot. But Viconia does care since the absolute threatens her personal power base. The hunt for the prism is her personal project.
From her journals we can deduce that Viconia does not have a high opinion of Shadowheart. She is resentful that she had to destroy her cloister in Waterdeep for her. Shadowheart proves to be a real pain to train. Viconia is also jealous of the undeserved favour Shadowheart enjoys from Shar. So she might have concluded that Shadowheart could become a threat to her, and work to undermine her (like by denying her the rank of justiciar). Viconia cannot defy Shar and get rid of Shadowheart in the open. But she can send her on a dangerous mission, which is a win-win for Viconia. If she gets the prism she improves her own power. And should the mission fail Shadowheart will suffer a convenient death in the service of Shar. There's also the possibility of hitting two birds with one stone and achieving both.
Shar seems none too pleased about any of this. Because should Shadowheart prove her loyalty, the first thing she does is send her to usurp Viconia.