Jarl Balgruuf seems to disagree with you, he talks to his steward about sending resources to Cyrodiil and that the city coffers are running short because of that.There's nothing in the lore that supports this. The ingame dialogues largely assert the opposite, i.e. that Skyrim is dependent on subsidies from the Empire.
She said nothing of the sort. She said that it was Nord custom to accept the challenge. That hardly makes it legal and regardless of whether one thinks it's not murder in layman's terms it's irrefutably high treason under Imperial Law to do any harm to an allegiated sovereign of the Empire under any circumstances.
Sybile Stentor says, and I quote: By the time we realized that Ulfric was here to challenge Torygg... it was already too late. By Nord custom, once the challenge was issued in court, Torygg had no choice but to accept.
If the duel had been illegal he couldn't have issued it in court. And duels have been a custom of the Empire in the past, for example in Morrowind where you could only reach the highest rank in the Imperial Legion by dueling the Knight of the Imperial Dragon to the death. And if duels were illegal, the challenger(radiant) would have been attacked by guards even if you accepted the duel(he is attacked if you refuse, bcause he "won't take no for an answer"). Everything points to duels being legal.
As a sidenote, Stentor also says that if Torygg had turnd the challenge down, Ulfric could have called for a new Moot. Seems to be a strange practise to follow an illegal duel, don't you think?