Why do all companions remove the force armor helmet when they entered into the force armor for the first time? And Paladin Danse don't wear his T-60b helmet at all. Is there a some secret, for instance helmet is invisible, it gives protection, but not visiable for better interaction or so?

Well, I checked Paladin Danse. Without helmet he has 1160/885 armor (phys/energy, without his small cap). With my helmet T-60b he has 1360/1025. With his helmet in the Call to Arms he has 1400/1065. Thus he has type D unbreakable force armor helmet. Where is it? More to say. If I give him my armor plates, he has now 1160/825 (with helmet), exactly as I. If I get back my armor, he will has... 1160/825, but will looked like he is in exoskelet without armor plates. So he still has my invisible armor. Well, I check it with only helmet. I removed his cap, give him my helmet, equip and get it back. And now he has 1360/1025, as with my helmet, but without it and in looking good his own armor.

He can survive having a rocket motor lit off right abvove his head...even without his helmet on......pretty impressive armor, I thought.

O no, in this quest he is in his helmet.

And it's indeed impressive armor. Cure has 0/0 armor, Cosworth 35/15, Dog 0/0 (but may has dog armor), others - any wearable. But paladin Danse unbreakable armor >1000.