Maybe I don't know enough about the internal workings of Facebook but Xbox was the perfect storm of a number of different initiatives that were going on internally at Microsoft at the time. their existing supplychain around peripherals coupled with the fact that windows PCs have always been the primary gaming platform of choice Microsoft was well positioned to leverage existing relationships in the industry to launch a dedicated platform.

I don't think so. For Microsoft it was natural to make the Xbox. They were involved in the PC so much, and the first Xbox was basically a PC trapped into a black and green colored box. Most of the work they did then was on software, which was their specialty in the first place.

Facebook has no direct connection with hardware, serious 3D gaming, VR or anything close to it. I fail to see how you can draw a comparison between the two. And the Xbox was not an acquisition, it was developed internally by Microsoft.