I agree mostly with your post except for the middle east. Culture plays a role in defining a race and whites are basically people with european heritage, both genetically and culturally. I know middle easterners and even indians can be considered caucasian but they're hardly white. There are exceptions though. It's not because of Islam, Albanians are white, but Saudis not really. You can make exceptions for some iranians, pashtuns and so on who at least speak an Indo-European language. But whatever.
Some very rough math:
200 million whites in the US
50 million whites in Brazil(debatable, the census give double these numbers but the large amount of christian arabs and light skinned mixed race are considered white there)
500 million whites in western europe(the EU has 510 million people, no clear race breakdowns, of course there are many non-whites there but western europe also includes other more white countries like switzerland and norway not in the EU)
28 million whites in Canada
25 million whites in Australia and NZ and other small islands
120 million whites in Russia
50 million whites in Belarus and Ukraine
100 million whites everywhere else/probably an underestimation(Argentina, Uruguay, Mexico, other latin american countries, South Africa, expats in China, Saudi Arabia or whatever)
Over 1 billion white people around the world.
There are many more people that are partly/mostly white in Brazil, Mexico, Cuba and the rest of latin america.
For comparison there are 1.3 billion Han Chinese.
1.6B muslims(of course they comprise many ethnicities including white)
Probably around 1B blacks(800 million people in Subsaharan Africa, 35 million African-Americans, 100 million brazilians with some african ancestry although only 14 million identify as pure blacks and genetics confirm most african brazilians are mostly european especially in the paternal lineage)