Your right with that first point, Ulic was sort of the military leader of the Krath, so he would likely lead a quick and brutal assault on Coruscant from Empress Teta. But even a few hours would be enough for Xizor to escape Coruscant, the Virago would also be fast enough to escape during the battle. He could then retreat to Mustafar (the Black Sun HQ we saw in TCW) and hunker down their. Ulic would then have to chase him there and face an organised armarda, as well as a possible incident with a gravity well generator en-route So Xizor will still be a threat while Kun is dealing with the academy.
1. Empress Teta is right next to Coruscant, and Ulic will be commanding the Krath. What would be the point of sitting Ulic at Yavin when his forces are light years away? He will be commanding the Krath, and will attack from Empress Teta. The speed at which they get to Coruscant will not allow Xizor to prepare anything besides rallying his mercs.
2. Exar Kun and the Massassi Warriors will be empowered by Malachor's Dark energies so the academy will be of little difficulty. Landing will be the hardest part, traversing the planet won't be incredibly difficult.
3. By the time Kun is done with the Academy, Ulic will have defeated Xizor. Kun will sense Traya on Yavin (using his advanced Force senses), which will make him contact Ulic (using telepathy, which he has done), and have him come pick him up. Then the entire Mandalorian and Krath War Fleet will attack Yavin. Now Traya is the one susceptible to bombardment.
Concerning Force sense, let us not forget that Traya was skilled in the use of Force concealment. She could shield herself from the senses themselves but also in the way Sidious shielded his presence from the Jedi Order. This is how she managed to maintain her disguise as Kreia. It fooled the Masters of the Jedi High Council, even when she was right in front of them, even when she revealed her identity their vision of her was clouded, so she could likely do the same with Kun, especially over such a distance. And you can't just pick someone up from the most hazardous planet in the galaxy. Ulic would just crash down with him. But I think Kun is capable of escaping, perhaps on a Basilisk droid? But he would still be forced to leave his warriors behind.
Oh and can you remind me again of where Kun displayed his power in Force sense, I remember you said in Kun's prievous Kaggath but I have forgotten. :P
And Maaurin, what is this amulet of death you speak of? And I think Traya would destroy the teachings on Malachor, or maybe even destroy the academy itself - she would want to give Kun no reason to linger.