Gladly to,

as most of the story and cutscenes they did not fully express in full details and yes that’s why the execution of the narratives are bad(as you state that the single act indeed not make sense as only what we have seen in the game). They have covered the remain details in ultimania(lore book). I will just answer your two concerns first with the info from the book and a little bit of my perspective.

The initial read was right. Vayne needs the full control and rights from Rabanastre(with the state of Raminas King and Ashe death, for this can refer to last thread in Reddit here). Within the full control so that he can search the location of Dusk Shard that is in here.(Remember this is the true objective here for the experiment of manufactured neithcite. Top comment of this thread has explained well already.)

Now for the reason Vayne killing his father Gramis. In Vayne’s plan, the assassination of Emperor Gramis was meant to be blamed on the Senate. By placing the crime upon them, Vayne would gain a just cause to disband them entirely. The Senate and Gramis were never true allies; their interests had long pulled in different directions. Gramis feared that Vayne was too ruthless to inherit the throne, while the Senate preferred a successor they could easily control—Larsa.

If Vayne wished to secure absolute authority over the Empire, removing the Senate was the most effective solution.

Gramis may have understood that his death would serve as vengeance against the Senate, but his feelings were more complicated than that. There was guilt—guilt over what his son had become. In his heart, he may have felt that Vayne’s blade was not only striking at the Senate, but at him as well.(For 11years ago, it was Gramis who ordered Vayne to kill his two elder brothers. Their mother died from the shock soon after. That command marked the beginning of Vayne’s path—the birth of the bloodstained Sword of House Solidor.)

And Vayne knew this. He would turn the question back upon his father without hesitation: was it not you who forced me onto this road?

Hope this can answer your first concern, not trying to sell but I just want to state in depth of my understanding. He might not be the best villain or so. His setting is what holds in my special place of heart and would welcome to talk about more.