Did any African nations participate in either of the World Wars?

Just finished going through Churchill's memoirs again. They're an excellent source if you're looking for an overview of what the world was up to - the British had interests everywhere and just about everything gets commented on at some point.

Taking it point by point:

-Australia was not a major theater of combat. They provided several units to the British and were a major participant in the campaigns in North Africa. After the Japanese entry to the war, they were threatened by the Japanese advance in the south Pacific but the Japanese were not able to advance past Indonesia. Churchill comments a few times on the prevalence of partisan politics in Australia, mostly in the context of them wanting to withdraw troops from action in the ME to defend against the Japanese.

-South America was not involved in the war, beyond a couple of minor fleet actions hunting down German commerce raiders.

-Indonesia was a Dutch colony at the time and was conquered by the Japanese. Not a lot of combat actually within its present boundaries after the initial Japanese conquest, mostly including some of MacArthur's later campaigns predating the invasion of the Philippines. Lots of war-time starvation. They declared independence after the war.

-Japan conquered most of IndoChina. They didn't make it all the way to India (partially due to British resistance and partially to a lack of real interest in the territory). British campaigns managed to eventually re-open the Burma Road but suffered from a lack of priority and supplies. Churchill's opinion was that it wasn't a good area to campaign in - jungles suck, and if you win the war you win them anyway - but the US placed high importance on keeping China in the war and so the British went along with it.

-India itself never saw combat, but British/Indian units fought in many of the major theaters of the war with distinction, especially in the Middle East and Italy. Churchill's definitely not a good source when it comes to India (he was very much against Indian independence and he is remembered much less warmly there than basically anywhere else, possibly excepting Russia!)

-There were several minor campaigns in Africa aside from the north coast, the biggest one being the liberation of Abyssinia (modern Ethiopia) from the Italians.

-South Africa contributed some resources to the UK, including several pilots who would go on to become aces.

-There was a secondary theater in Iraq as a German-backed insurrection was fought off mostly with RAF units. Tehran had a minor insurrection at one point and was occupied by the British and Soviets, and a railway built through the region became a major route for Allied supplies reaching the Soviets. Syria was... a big mess as it was caught between the Vichy French, the British, and its own independence movement. Palestine was a constant running sore for the English (in the sense that they had to keep a lot of troops there to maintain order, since arming the Jewish settlers was against previous imperial policy, something that Churchill opposed but couldn't quite get resolved...)

-One thing to keep in mind for this question is that there really weren't a lot of independent countries in the areas you mention. A great deal of Asia and Africa were colonies of the European powers, with independence being pretty uncommon; that occurred afterward, as the European powers were mostly exhausted (or defeated) and the US and Soviet policy was to encourage independence over continued colonial occupation.