There wasn't except allusions that Siuan felt guilty for Leanne's fate, because Leanne would have none of that and always stood by her decision to cover up Siuan's secret dealings with ta'veren the Hall deemed dangerous. She didn't know the secrets, but she very well knew Siuan was secretely scheming with Moiraine and others, and she turned a blind eye to that by choice/loyalty. The Hall might have considered her all the more guilty/irresponsible for covering up schemes she knew were ongoing but didn't know the nature of, except they involved individuals and situations that worried the Hall.

There wasn't any trial because Alviarin well knew that the "stilling offenses" against Siuan and Leanne (freeing Taim etc. - Elaida can't lie, so she must have gotten false evidence of some kind or another to bring up that accusation. Likely Alviarin cooked up something about sisters Siuan had sent to capture Taim not unlike the lies Siuan cooked up later against Elaida and the Reds) were invented and would fall apart in a trial in which Siuan, who can't lie, could flat out answer any questions from the Hall about that, leaving only her secret dealings with the ta'veren and having made all sort of executive decisions concerning TDR without involving the Hall (and where she was within her power and where she wasn't is a very murky area at best. We just don't know.). Siuan's actions probably justified her removal from office, or the Hall would have tried to blackmail her into becoming their puppet, but it's the stole Elaida wanted, and the others were seemingly blinded by the influence over the course of events and decisions they thought they'd get by electing her in such a weak position, as evidenced by their "council" later on, and to make that happen they were quite content to break the rules about Siuan's trial. They probably suspected all along that Siuan might wriggle out of the accusations if they let her defend herself, at least enough to deadlock the Hall. Their minds were made that she had to go and Elaida had to be elected in her place, so they overlooked the law. The sentence of stilling was most likely pronounced not with Justice in mind, but in the full knowledge thay their position was weak and they had make sure there wasn't any way to undo what they were about to do. They probably didn't foresee the split, but they sure foresaw that a pro-Siuan faction would fight back, but they thought by stilling Siuan they killed its chances in the bud and they would reconcile themselves to Elaida's election. The other related reason to expedite Siuan's trial was of course that Elaida's cabal didn't want to risk the full Hall to be assembled, so they expedited the removal, the election, the secret trials and sentences all in one sitting. The sentence itself was apparently carried out in secret as well.