How can I turn the sentence
Ich habe das nicht machen können.
to a question? And In which situations would I use
Ich habe machen gewollt?
How can I turn the sentence
Ich habe das nicht machen können.
to a question? And In which situations would I use
Ich habe machen gewollt?
I am not sure if understand your question question right but
Habe ich das nicht machen können?
would be the most direct way to form your first sentence into a question.
Ich habe machen gewollt
you better not use at all since it is wrong. A correct sentence would be
Ich wollte X gemacht haben.
which would use if you would have liked X to be done (by you).
First, examples of questions in first person are a bit awkward, as you had been asking yourself then. Let's put it into second person.
Ich verstehe. Du hast das nicht machen können.
I understand. You haven't been able to do it.
Making a question out of it is simple:
Ich verstehe dich nicht. Du hast das nicht machen können?
I don't understand you. You haven't been able to do it?
It's that simple. The intonation of the second sentence changes (voice up at the end of the sentence instead of voice down as usual.)
In addition, you can make a proper question of it by putting the finite verb at the first position. It doesn't matter whether it's an auxiliary or not
[…] Hast du das nicht machen können?
The meaning is (roughly) the same. Emphasis changes from Du to Hast, because the first word in the sentence has more emphasis. But that's something you could also take care for by intonation.
Your second sentence is wrong - The perfect tense construct for modal verbs (like "wollen") follows a special rule that asks for a Ersatzinfinitiv instead of the perfect participle of the modal verb. So instead of saying
Ich habe machen gewollt
you need to say
Ich habe machen wollen
like in your first sentence that has a proper infinitive ("können").
And questions in the perfect are being built from such sentences by slightly changing the word order (put the predicate in front):
Habe ich machen wollen?
There are two general ways in which German turns sentences into questions: one being the polar question (or yes/no question) and the other being nonpolar or interrogative questions, i.e. those that use a question word.
To turn a normal sentence into a polar question, simply place the verb in first rather than second position and proceed as normal.
Ich habe das nicht machen können.
Thus, this sentence would be turned into:
Habe ich das nicht machen können?
To form an interrogative question, you would generally choose your question word as applicable, place that in first position and proceed normally (keeping your finite verb in second position):
Was habe ich nicht machen können?
Finally, there is also the concept of an intonational question; i.e. you are saying what is in fact a normal clause but using rising intonation making it into a confirmational question (‘that is true, isn’t it?’). For that type of question, do not change anything; just add rising intonation.
Ich habe das nicht machen können?