Wow, Wuk Lamat is really single-handedly ruining the DT story...

[Astronis]

I also find it odd how readily everyone accepts Gulool Ja as the new King? of Solution 9...

Yes Zarool Ja picked him/gave him authority. But Zarool Ja is also the king who murdered his own citizens, and he was only given the position of King because he made a deal with Sphene to get her the souls she needed. He did not deliver on that promise, he failed to get her the souls (he had the opportunity, attacked and got 50, but then let his pride get in the way and stopped. I assume as she planned to move through all the shards and source 50 was not enough), and as mentioned he then went and killed her people. Why exactly is everyone so happy with honouring the last wishes of someone who has proven by failing his end of the bargain and killing people that he is unfit to rule.

Because he's Wuk Lamats brother? And they want to try and soften her killing him by being able to abide by his last wishes and play happy families with what seems fairly certain to be a clone of him?

Why do the people of Solution 9, who seemed to have no part in Zarool Ja attacking Tural and no idea what Sphenes end goal was, have no say in their own future and instead have to abide by the choices of the false king who slaughtered them? Why weren't they given a chance to gather together and figure out what they want to do next themselves in terms of government and a new ruler that Gulool Ja could pass on the authority to.

Everyone was not happy about it. That's something called out directly by Erenville. That said, Alexandria's government is a computerized monarchy. Zoraal Ja essentially passed Alexandrian admin rights to Gulool Ja; unless Gulool Ja passes them to someone else, they are his. No one can take them, and no matter how unhappy anyone is, he's the king. He's got root access to Alexandria. It's got not a thing to do with honoring anyone's last wishes. I am positive this is something that will come up in the patches, since it's called out loud and clear that the Alexandrians aren't terribly pleased with the current situation. Wuk Lamat derping her way into annexing Alexandria as a protectorate is very badly begging for follow-up. It HAS to bite her in the ass.