Would 'she wants to have the clothes' require 'att' somewhere? e.g. Hon vill at ha...? (is that why I got it wrong?)
No, it would be OK, it's just that "she wants the clothes" is the normal translation of this (you can't skip ha in Swedish). You can report missing "ha" and we'll add them.
PS and you can't add an att in the Swedish sentence.
The only auxiliary verb you can put 'att' after is kommer. All the others, such as 'vill', 'kan', 'ska', 'borde', etc can't have it.
vill is 'want' with verbs: Jag vill äta 'I want to eat', but vill ha is 'want' with nouns: Jag vill ha mat 'I want food'. Hope this helps?
äter is the present (like 'eats') and äta is the infinitive, but it hasn't been taught yet at the point in the tree where this sentence is. But when you say in English I want to eat, 'to eat' is also an infinitive, so it works much the same.