Yup, many Tutsi had to flee to Uganda. The Rwandan (Kigali) infrastructure is head and shoulders better than the Ugandan (Kampala) infrastructure today.
Yes to the first sentence, no to the second sentence.
Unsurprisingly, this all rooted in CaCs being CaCs. When the CaCs first got to the region Tutsi and Hutu were not ethnicities, just class distinctions. There were a bunch of different clans, but CaCs (Belgians) made up those two ethnicities/races using racist pseudo-science. Here’s a couple pics from the Kigali Genocide Memorial (3rd pic is in the memorial, but not taken by me):
So they divided the population by these races declaring the Tutsi more intelligent and worthy of their “aid” thus making them rich and powerful, and of course causing the larger Hutu-deemed population to become jealous of them. And it spiraled from there (including other CaC influenced accelerants, especially from the French). Resentment grew to the point where Hutu felt they needed to expel these wicked Tutsi people and nonsense like those commandments were created.