Yes, just like in the previous games, Paralyze Palm works with any unarmed weapon.
I guess, but trying your hardest should already be fun, without me having to come up with my own challenges :\
If a sneak attack critical hit to the head from an AMR didn't take down a deathclaw, it be to overpowered to face any other way. Unlike most games Fallout greatly rewards stealth without making it an absolute requirement.
Lets think about this to battle deathclaws we use stealth, high vantage points, and a big *&)*%#) gun. Why are we so careful when fighting a deathclaw why don't we charge right in and beat it down with a machinegun or a melee weapon like any other creature? Because we know a deathclaw can quickly rip you to pieces.
If they weren't the baddest mother *)*%)*% in the wasteland we wouldn't go to all the trouble to cheap shot them whenever possible and avoid a stand up fight.
I think it was harder to kill Deathclaws in Fallout 3. Maybe it was because the max level was 20, but in order to 1-shot kill a Deathclaw in Fallout 3, I had to use Psycho, and manually aim at the head. I don't think VATS allowed you to have a 95% accuracy at the head from long range. So if you missed, you would be dead meat because the Deathclaw would be alerted to your presence. I think maybe that's the kind of difficulty the OP was looking for.
Yes it allowed 95% to the head, the %%% were much higher in FO3 overall you never got the sniper perk did you? Killing a deathclaw in one hit was quite easy, same way as now, sneak attack critical to the head with a high powered rifle, as VATs was much more potent you could safely do this from close range.