1) I'm well aware of the tradition surrounding the duel, but you have the Nords split between it. Some considering it unfair, dishonorable and simply murder. The Empire doesn't have to recognize anything about Ulfric. Ulfric killed Torygg, fled to Windhelm and declared war on the Western Holds. The Imperial Legion stepped in when the Jarls began picking sides. It is a Civil War. It is illegal by Imperial law, something I had just proved by a lore source about Imperial law and justice.
IS the Solitude Court guilty of Treason too? Because they had to let it happen because of NORDIC LAW which details how to solve those issues?
Sometimes lore is only as good as the person seeing it.
No. It is an ancient Nordic tradition, challenging the High King or Jarl for their title. Something that probably hasn't been used since the First Empire of the Nords, which Alvor mentions when the Jarls start killing each other we're back to the bad old days when the Holds would fight each other.
Had Torygg refused by Nordic tradition he could be voted as no confidence and lose his throne in theory. Torygg accepted the challenge because it was questioning his honor, Nords when it comes to their personal honor can act without thinking.
Torygg's Court didn't allow it to happen, it happened very quickly. Ulfric issued the challenge, Torygg jumped up and accepted it. Ulfric shouted Torygg and killed him either by his sword or shouted him apart depending on which story to believe. Torygg had some martial ability, he wasn't defenseless, but that didn't matter because Ulfric used the Thu'um.
Ulfric didn't announce he was going to kill the High King until the last minute. Everyone believed he was actually going to ask Torygg to declare independence, which Torygg was in favor of.
It was viewed by many Nords as murder and dishonorable. When it comes to a duel between Nords, one generally thinks of skill by steel.
By Imperial law it was illegal, Ulfric knew it was, he was once a Legionnaire so he would have great knowledge of the law. He fled from Solitude, Ulfric killed Torygg to have the war. Torygg was merely used as a message to the other Jarls.
"Ulfric founded the Stormcloaks years ago, as a sort of private army to advance his ambitions. He's always used the ban on the worship of Talos to stir people up against the Empire. He never succeeded in getting much support, so a few months ago he murdered the High King! That got the Empire's attention." - Hadvar
"Walked right into his palace in Solitude and killed him. Shouted him to death, if you believe the stories. That's what started this whole war. The Empire couldn't ignore that. Once the jarls start killing each other, we're back to the bad old days." - Alvor
"Torygg was merely a message to the other Jarls." - Ulfric
Edit: The problem with Torygg was his honor, he took the challenge. It doesn't make it right, nor does it absolve Ulfric.