“We asked whether the war had been finished” is not a question, so it should not have a -ne on the first word. “whether” can be translated by a word such as num.
confecisset is the right tense, mood, person, and number, but the wrong voice. “had been finished” calls for the passive voice.
He ran so quickly that no one could catch him
tam celeriter cucurrit ut nemo eum capere possent
the subject of your result clause, nemo, is singular but the verb is plural. There is a rule that subjects and verbs must agree in number.
They have come in order that they may conquer us
venerunt ut nos vincant
correct
We shall ask what he is doing
quaeremus quod faciat
quod is a relative pronoun; you need to use the interrogative pronoun quid.