1. He will be able to ride a motorcycle.

2. He will be able to take a motorcycle.
3. He will be able to ride a motorbike.
[Can we use the verb 'take'a s in #2?]

4. Only buses will be allowed to travel on the roads.
5. Only buses will be permitted to travel on the roads.
6. Only buses will may travel on the roads.
7. Only buses will be permitted to go on the roads.
[Because we can not use the structure 'will may', we need to use #4 or #5. Am I right? Can we use 'go' as in #7?]

In 2, "take" implies that he removed the motorcycle from wherever it was -- or maybe that he stole it.

1 and 3 are fine.

4, 5, and 7 are fine.

6 would be fine it you used "will" or "may" (depending on meaning), but not both.