Hello! These questions are a little tricky, so forgive me if it seems like I'm meandering. Yes, the Japanese military did enlist conquered locals, but this happened in a wide range of contexts and generally at the point of a gun. Most notably, at least fifteen million forced laborers (the majority of them Koreans and Chinese) served the Japanese wartime empire by working in mines and factories or building roads, bridges, and air fields. Countless perished toiling under appalling conditions, especially in Burma. Many others were left disabled and abandoned at the end of the war. Few received any form of compensation from the Japanese government and corporations that had exploited them.

In addition, the Japanese recruited or conscripted Korean and Taiwanese civilians as "military support staff" (gunzoku), also acting as labor units. They officially stood outside the military hierarchy, or at least at the very bottom: "military men, military horses, military dogs, and military support staff" (gunjin, gunma, gunken, gunzoku). The military sometimes called upon women to serve as nurses, while the less fortunate became forced prostitutes, known euphemistically as "comfort women" (ianfu). Aside from that, auxiliary soldiers (heiho) bearing such titles as the "Java Volunteer Defense Corps" or "Burma National Army" helped police and garrison the conquered territories of the Co-prosperity Sphere.

I'm more familiar with the situation in China, where the Japanese equipped upwards of a million troops nominally under the command of various puppet regimes, most prominently with Manchukuo and the Reorganized National Government of China in Nanjing. In theory, the puppet troops would protect railroads, villages, and other strategic points against guerrilla attacks, thus freeing up Japanese troops for more important operations. There is plenty of anecdotal evidence, however, of collaboration between the puppets and guerrillas, or at least of "live and let live" agreements. Chiang Kai-shek's Nationalist government (based in the wartime capital of Chongqing) even claimed that most of these "puppet" troops were secretly loyal to the Nationalists. This probably isn't true, but it did mean that the Japanese would have to feed and pay entire armies that the Chinese otherwise couldn't afford to. In fact, after the war, both the Nationalists and Communists (though mostly the former) assimilated them into their own armies.

Let me end with a story, as recorded by the American journalist Agnes Smedley, that might encapsulate the answers to your two questions:

Late one afternoon my secretary and I were returning from the market town of Changjiaji when we fell in with a company commander and his squad of soldiers returning from the front lines. The commander told us that on the previous night, as his company was crawling lip a hillside to storm an enemy position, his men heard a Chinese voice somewhere above them say:

"Lao hsiang [countrymen], come no farther! We have orders to use poison gas!"

"Traitors!" the company commander exclaimed.

"There is no other way," said the voice.

The company crawled down and around the hill, intending to attack the position from the rear, but found itself completely surrounded by a whole battalion of Manchurian Chinese puppet troops. The puppet commander told the company that he would give them back their guns if they would retire at once. He said that his men would fire high in the air. "You are traitors!" the company commander again exclaimed, but the puppet leader answered that when the puppets were conscripted by the Japanese in Manchuria, their families had also been registered; if they deserted or refused to fight, their families would be killed.

The commander argued with the puppets, telling them that the families of loyal Chinese were also in Japanese-occupied territory that all Chinese were men without homes. He pleaded with the Manchurians to come with him. The puppet soldiers stirred uneasily, and the company commander said that if it had not been for the officer they might have deserted. Even the puppet commander had hesitated and his voice had sounded deeply troubled as he told the soldiers to take back their guns. Before leaving he had said: "Don't go in that direction; there are machine-gun nests there, and the gunners are Japanese."

In this case, we find that not only had the Manchurian troops been conscripted, their families were also being held hostage. This is one way the Japanese obtained more soldiers and ensured "loyalty."

There's not much English-language literature on this topic, and I'm still doing my own research as well, so I apologize if you don't find this response entirely satisfying. I hope it's informative, nonetheless! :)

With the Germans, you get a couple of different "models" for foreign service.

Specific to the Eastern front, you get a few different layers:

• Units raised from groups / areas that were historically antagonistic to Soviet rule. Some of the Cossack units would be a prime example of this category.
• Local civilians or Soviet military deserters that volunteered and were integrated into German units generally in support roles. They wore German uniforms, but with distinctive insignia, and tended to serve most frequently in non-combatant roles: stretcher bearers, drivers, and so forth.
• Soviet prisoners of war were sometimes pressed into service as well, doing somewhat "dirtier" versions of the jobs that the individuals in the previous category would have been employed in. Helping out clean up after the horses, helping out with the kitchens, and such. Prisoners that volunteered tended to get a better lot than those that were merely assigned to those duties.

Outside of the Eastern front, it was generally much more volunteer based. You had individuals from a number of different countries that willingly enlisted out of political sympathy for the Nazi cause. Some were anti-communists, a few were genuine fascists, and some were more "enemy of my enemy". Early on in the war, it was usually people that came from populations that were ethnically preferred by the Nazis (Scandinavians, ethnic Germans, and the like). There were some that were able to assimilate into regular German units (ethnic Germans from Poland that were culturally German and spoke the language fluently), and others were organized into specific units based on a given nationality. There were a number of SS Divisions that were set up in this manner. As the realities of the war gradually dawned on the German leadership, you began to see numerous non-Germanic SS formations formed as well.

Curiously enough, some of the last holdouts in Berlin at the close of the war were French SS volunteers.