How many Chetniks were there under Mihajlovic's command? How many were there in other factions? How many people were in Nedic's guard and other similar "German-inspired" formations? How many Partizans were there and what percent of them were Serbs, Croats, Slovenes, (of course there were also Bosniaks, Albanians, and other small numbers of ethnic groups living in Yugoslavia)?
[...] By the way, is there any book in English about Balkans during WWII which you would recommend? Thanks again.
The numbers varied throughout the war. The leading authority on the WW2 Royalists in Serbia, Miloslav Samardžić, says that in the spring of 1944 there were "over 100,000" Chetniks* under Mihailović's command. Nedić's gendarmerie numbered around 20,000, and there were about 8,000 or so men loyal to Dimitrije Ljotić, a fascist who eagerly collaborated with the Germans.
Samardžić also says that Serbs made up the vast majority of the Partisans. When you hear about "Croatian" partisans and "Croatian" brigades, he says, those were actually Serbs from territories called Croatia, not necessarily Croats.
The most commonly used figure for Partisan numbers is 800,000. It comes from official Communist history. Even if we assume its accuracy, the figure comes from late 1944, when many Chetniks as well as Domobrani (Croatian regulars called up by the Pavelić regime) and Italians had joined up. (According to the same source, the partisans had suffered over 300,000 casualties during the war, mostly in the open battles of late 1944 and early 1945.)
I have heard good things about Michael Lees' "The Rape of Serbia" (subtitled "The British Role in Tito's Grab for Power 1943-1944"), published in 1990. I haven't actually managed to obtain a copy, but I've been following a lot of work in Serbia about the intrigue and power games involving the British, Tito, Mihailović and the royal government in exile. The picture that emerges is that the Brits sidelined the royal government, cherry-picked one of its members (Ivan Šubašić, the pre-war ban of Croatia) to sign a treaty with Tito, then bullied the young king into issuing a radio endorsement of Tito as the supreme commander of the resistance.
It wasn't just the Serbs who were used then abandoned by the British. The Poles and Czechs who escaped to the West were similarly betrayed when all of Easter Europe was given to Stalin. And then there was Operation Keelhaul...
(* The proper name for this force was the "Yugoslav Army in the Fatherland")