Yes, back-to-school is hyphenated when used as an adjective phrase before a noun, such as "back-to-school shopping."
Yes, "school-age" is typically hyphenated when used as an adjective before a noun (e.g., school-age children).
The term "high school" is a compound noun, with a distinct meaning (secondary education) separate from simply a school that is high. It can also be used as an adjective/noun adjunct for things associated with high schools (e.g. high school teacher) and is usually not hyphenated.
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, "pre-school" is a hyphenated word.
Fine-tune is an 8 letter hyphenated word. High-tech, half-mast, half-moon are additional hyphenated words.
Heart-to-heart and half-baked are hyphenated words. Additional words include high-minded.
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.
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.
No it's not hyphenated.