When do I use würde + infinitive in reported speech instead of Konjunktiv II
I've nearly kind of mastered when to use Konjunktiv I and Konjunktiv II in indirect speech, but then I learned that sometimes you have to use würde + infinitive instead of Konjunktiv II and I'm really confused why and when you need to do this!
Würde + infinitive is just another way to built the Konjunktiv II. You can use them interchangeably.
In my experience native speakers use the würde-form almost always while speaking, because it's easier and we are kind of lazy (that's also the reason why we use the Perfekt-tense instead of the Präteritum while speaking).
But it's also common to use it in writing to avoid repetition, to avoid verbs where the Konjunktiv II is complicated or just because you're lazy.
Edit: Oh, I almost forgot: You also use würde + infinitive when the Konjunktiv II would be the same as the Präteritum form of the verb.
e.g. "Er hat gesagt, er wartete." - here wartete could be Präteritum or Konjunktiv II, so you use "Er hat gesagt, er würde warten." instead.