Heh!
You may indeed go to both. I can help a tad with the Princess- you have no specific reason to see her, but the point was that you were earlier casting suspicion on Annuneryn, and just in connection to 'stuff he had done', Argentis saw him earlier waiting to see the Princess.
You're a strong guy, Anglomir, and the crowd (being mostly common men themselves, for such an event) favour you well, even though you are not one of their own. You look the part for a victor in such a test.
Walker- those Elves are being all concerned/snooty over who the corpse was. Apparently they feel the meaning of his identity may be important?