Your speculation is correct for Vol 1, the triaxial design represents the 3 Paravian races AND the ‘three stages’ that down stepped them into incarnate existence…
You are correct with Ships and Warhost and Fugitive Prince.
Grand Conspiracy - 4 elements, yes, also: something ELSE but I can’t mention it - look for it in Song of the Mysteries. Also count the interlocked conflicts/you may not know them all in this volume, however. Also the 4 governing agreements, the concords that ‘rule’ Athera - though you may not know all of them in this volume. I will leave you all to figure it out!
Peril’s Gate is Raven and raven, I will leave you all to figure that one out, too.
Traitor’s Knot - you are correct, and if you read the book you will KNOW why the sword image recurs in this volume.
Stormed Fortress - you are partly correct, the bull is the s’Brydion ducal seal/Alestron’s history is considerably OLDER than their tenancy in the Third Age.
Initiate’s Trial is taken from the focus pattern at Fiaduwynne, where Gestry makes his decision to follow Dakar’s battle plan.
Destiny’s Conflict relates to the haven at Los Lier.
Song of the Mysteries is the fifth lane focus circle pattern located in the ruin of the King’s Tower foundation at Ithamon.
There was deeper discussion of some of the symbolism in one of the archived discussions for the series found in one or the other GoodReads discussions, either in Beyond Reality or the Fantasy Buddy Reads group, or the Fantasy Book Club group, not sure which.