Donne quelques exemples pour pouvoir te répondre ! :)

1-"De temps en temps" is an expression, you can't change it. But what you can do is using another expression as "Quelquefois" (yes, it is always attached !), then you would have "Je la vois quelquefois", meaning, sometimes. 2-Here, yes, the meaning is belonging to. The professor is belonging to the école, and la voiture to Marie. But if you had for example "Un professeur d'école", it would be a status, a fonction if you want. And also, never use "le" after "de", like you can't say "La femme de le patron" but "La femme DU patron". 3-"Une tasse de café" is a "Cup of tea", and "Une tasse à café" means "A cup for tea", see the difference? 4-In this case, it's exactly the same. But in metaphorical phrases, you would use "de" instead of "en", like for example "La femme de fer" (We used to call Thatcher like that), meaning "the strong woman", because if you say "La femme en fer", it means "the woman made of iron". See? 5-You can say "C'est la personne la plus gentille au monde !", you don't need "de". But in "copie d'examen", you do, and it has nothing to do with superlatives ! (Difficile*, not difficulteuse) 6-Un sac de quoi? de maquillage, une voiture de quoi? de sport, etc = "of what?". For the quantity, it's expressed by "beaucoup", and not "de". "De" in your sentence just introduce the plural, nothing more. "Il y a* beaucoup de personnes; il y a une seule personne" Another example "Je vois un chat; je vois des chats; je vois une centaine de chats; je vois des centaines de chats" = I see a cat. I see cats. I see a hundred (of? not sure about it) cats. I see hundreds of cats. 7-"De" in here means "To" or in certain cases "Of", guess which one of them do we apply in the following examples ! Je suis content de faire votre connaissance, je suis heureux d'être à tes côtés, je suis satisfait de ma journée, je suis fier de moi, je suis curieux de savoir, etc. 8-If you see "De" after verbs, it essentialy means "About". Let me know if you did understand !