"Hoeveel jassen hebben zij nodig?"
Translation:How many coats do they need?
The case of "raken aan" is simple: the word is generally written "aanraken" (as one word) because that's the infinitive form of the verb, and the infinitive forms are generally considered the most "basic" verb forms in Germanic, Romance, and various other languages. Furthermore, verbs like "aanraken" are called separable verbs; they are composed of a stem verb (in this case, raken) and a particle (in this case, aan). In some sentences, the two parts appear together as one word (e.g. "Ik wil de paard aanraken"); in others, they are separated (e.g. "ik raak de paard aan"). I see that you've studied some German, and German has separable verbs, too!
Regarding "nodig hebben", I don't have such a clear answer, but I do know that the same word order is frequently encountered in German. As a native English speaker, this word order was weird for me, too, at first; however, after some time with German, I began to see that it really just feels natural. Perhaps I just got used to it! Maybe someone else can provide a more definitive explanation, or maybe it's just a convention that has no convincing explanation!
Finally, note that "aanraken" only has one 'k' because the verb – in all its forms – is spelled such that the vowel after the 'r' is long. In forms such as "aanraak" and "aanraakt", the 'a' after the 'r' is doubled to maintain vowel length. Similar spelling changes to maintain vowel length are found in other parts of speech, such as in adjective inflections (e.g. geel→gele) and in noun pluralization (e.g. schaap→schapen; schildpad→schildpadden).