If you're using "after-school" as an adjective (e.g. I participate in an after-school program -- after-school is describing the kind of program I participate in), then it is hyphenated.
If you're using "after school" as an adverb-noun phrase (e.g. Meet me after school -- after school tells when to meet me), then it is not hyphenated.
Yes, "school-age" is typically hyphenated when used as an adjective before a noun (e.g., school-age children).
Yes, "pre-school" is a hyphenated word.
The hyphenated non-school would be correct, but would be an unusual usage.
It is not hyphenated.
The term for an educator can be one word, "schoolteacher."It also appears less frequently as a hyphenated form school-teacher.
No it's not hyphenated.
Motorcycle is not hyphenated
As a statement of a time, it is two words, as in "Come see me after school."As an adjective, it can be one word, as in afterschool practice, or afterschool meetings.
words are only hyphenated when they have a separate meaning when separated than they do when hyphenated
No, "hardworking" is not hyphenated.
Yes it should be hyphenated.
It can be. Some words can be seen both hyphenated and non-hyphenated.