The Aruch Laner suggests that the halacha that beis din may not tell someone that this is permitted is only if the person is asking if it is permitted to kill. Pinchas was not asking if it was permitted to kill, of that he was certain; rather he was asking if he could become tamei. Moshe saw with ruach hakodesh that he would not become tamei and thus told him to go ahead with the act.
We can suggest that the same can be applied for the question of sakanas nefashos. Perhaps that is what Pinchas was asking of Moshe, and Moshe answered him that a miracle would be performed for him. Therefore, Moshe was allowed to answer him and Pinchas was allowed to act.
I would like to suggest another answer to all of these questions. The halacha of kana’im pogim bo is exclusive to genuine kana’im who wish to avenge Hashem’s vengeance. It is exclusive to them because if one is not genuinely bothered by the disgrace that is occurring to Hashem he cannot act on it. One who is performing such an aveira is not chayav misa. In beis din he is not considered a dead man, as there is no sentence against him. Yet, if one is genuinely appalled by the disgrace, Hashem allows him to avenge on His behalf.
A mashal is given to a situation where someone in public begins severely disgracing another person’s mother in front of him. Will that person stop and ask and think about if he may stop him and contemplate all the different ramifications? No, he will act swiftly to stop the embarrassment. The same is with the halacha of kana’im pogim bo. A kanoi must be so enraged that he does not care about any other violations he may transgress, he is solely focused on stopping the disgrace of Hashem.
This is also the explanation that is given why beis din must forbid someone who comes to ask if he may carry out kana’im pogim bo. If he is asking questions, it does not bother him enough, and he is not the man for the job.