These sentences are fine, because the -ing form is used as an adjective:
"She reached her hand out, wanting to touch him..."
"Not wanting to talk about it, Clary turned..."
What your English teachers probably meant was that ordinarily we do not use these stative verbs in progressive constructions, like this:
"I am wanting to ask you how ... "
"I am liking this job very much."
But sometimes the 'state' which these verbs designate is conceived as subject to change over time; and when that is the case a progressive construction becomes acceptable. In your last example, for instance, the state is about to come to an end:
"I have been wanting to ask you how ... "
Or in this case, the state has been increasing over time:
I am liking this job more and more every day.
Jez objects that ‘native speakers might well say "I am liking this job very much."’ Perhaps so—the progressive construction has been steadily increasing its scope for 300 years now, and it is possible that the punctiliar sense on Facebook has definitively ‘unstatived’ like. But I would not expect to hear this except in a dynamic context as “I’m liking this job now”.
So I would advise Learners not to use the progressive construction. The stative sense is still built in to the word itself, and you can’t sound wrong if you use the simple present; but in some contexts you may sound wrong with the progressive.