1. He will must go to Japan. (X)

2. He will have to go to Japan.

3. She will may go to the amusement park.(X)
4. She will be allowed to go to the amusement park.

5. He must can speak Chinese.(X)
6. He must be able to speak Chinese.

7. He may must parctice speaking German.(X)
8. He may have to practice speaking German.

9. He may can go abroad.(X)
10. He may be able to go abroad.
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In each pair, is the second one grammatical?

yes

The second one is grammatical. The first of each pair is not.

yes

Yes, in each pair, the second sentence is grammatically correct. The first sentence in each pair contains modal verbs (will, may, must) followed by the base form of a verb (go, may, can). However, in English, modal verbs are followed by the base form of a verb without the addition of another modal verb. Therefore, the correct sentence structure is to use the modal verb + "have to" or "be able to" + the base form of a verb.