I can answer your question on the justification of the annexation of Wales, and the shortest possible answer would be: There wasn’t one.

To elaborate, William I didn’t have any sort of justification or casus belli for invading the Welsh kingdoms from about 1070-1081, he simply wished to protect his frontier against kings who could easily ally with anti-Norman forces in his country.
The Domesday book contains the best example of this sort of reasoning, when describing the lands of Osbern Fitzrichard (a marcher lord in Powys): “He has what he can take - nothing more”. Demonstrating that the only obstacle to taking more land in Wales was their ability to physically take it.

Much later, during the conquest of Wales, Edward I would provide a justification, however this was not a justification for taking the land, as again he (and all of his predecessors) could, and did, just simply conquer it.

When Edward attempted to conquer Wales in 1277 he provided a justification that the Prince of Wales, Llywelyn II, had illegally seized lands from his brothers (and in particular the brother that was assisting Edward, which is not a coincidence), but this was likely due to the fact that the Pope at this time was sympathetic to Llywelyn, and Edward might have feared involvement from the king of France.

So in summary, there was no legal justification for abolishing all the Welsh kingdoms during the conquest of Wales, and this was simply because the kings of England didn’t need one. If they could take and hold the land, then it was theirs. Later on, Edward I would provide a justification for his invasion, but this was likely due to his fear of outside sympathies and involvement.

Sources:
Davies, J. (2007). A History of Wales. London: Penguin, pp.101-108,150-151,154-155