Why is it that after certain verbs you use de. So like il est de nouveau seul or mon père a beaucoup de outils? When I see questions that really confuse I’ll post them but please answer.
"De" is a preposition with several purposes.
In "Mon père a beaucoup d'outils" the d' is a short for "de" that you would use before vowel sounds. It means my dad has a lot of tools. D' stands for "of".
"Il est de nouveau seul" means he is alone again. "De nouveau" means again, nouveau can't be employed alone here or it would mean "new" rather than "again".
I hope this made sense to you.
If you really want me to tell you all the details about this so be it. Though, they are extremely complex and you are better off not getting into the technicalities of such a "picky" language. But here you go.
There is no such thing as "De" is only employed when ___. It has so many purposes that it is nearly impossible to name them all. It can be a preposition, an article, it can modify the meaning of verbs, turn nouns into verbs sometimes even. Good luck with trying to make a set rule for when to use it, I'd say it is impossible.
It's not that "De" can only be used with certain verbs. Give me any verb, and I can give you a sentence where it is followed by "de". Let's take for example the verb "Venir" (to come). You would say "Il vient de Paris" (He comes from Paris) but you would also say "Viens ici" (Come here) See? Same verb, in one case you use de and in the other you do not.
And certainly the verb "Avoir" isn't always followed by "De". You can say "Je n'ai pas la moindre idée." (I don't have the slightest idea)
De in your case is used this way because it is employed as an article like "Des" and "Du".
"J'ai un verre de lait" I have a glass of milk. In that case "de" is used instead of "du" or "des" because it indicates a specific quantity. (one glass). If you hadn't specified or implied any quantity and just wanted to say "I have milk" You would say "J'ai du lait".
"Je n'ai pas de savon" as in I have no soap (I do not have soap). There's an implied quantity here, and that is "zero".
Another example of an implied quantity would be "beaucoup" (many)
remember "du" can only be used with uncountable nouns like "J'ai du courage" (I have courage.) With countable nouns, you must use "des" like in "J'ai des frères." (I have brothers.)
Again, it has multiple purposes and it is very complex if you want to study it like a rule. There are so many exceptions to these rules, as well. Such as "J'ai besoin de lait." (I need milk)
I would honestly not be surprised if you are just even more confused now. It's just the nature of the language, you're better off just learning to use it correctly by habit, rather than look so deep into the rules most of the time. The rules, rather than making the language easier to learn, will just leave you with more questions.