Do the LNG ships use the boiling off gaseous fuel for power? That is, do they take the gas as it boils off to power the ship or at least power the generators? If not, what a waste.

You can reduce boil-off of course by better insulation or take boil-off to power refrigeration equipment. (or both) In any case, it's some mighty cold stuff to have to ship. It would be better to turn the gas into gasoline then put it in a tanker at the source, saving the energy to refrigerate it. Of course, that doesn't help our NG woes.

They use the no longer L NG as fuel.  AFAIK, they pull with a full cargo on oil and then add NG as it boils off.  By the end of a long voyage, they have too much free fuel to use.

Thicker insulation means less LNG (inside diameter shrinks as walls get thicker).  The whole purpose is to deliver NG and the optimum point is found in design.

Note that the "optimum point" for Nigeria to Spain is quite different than for Qatar to East or West Coast US (thicker for US I guess).  So misusing a thinner insulation LNG designed for shorter hauls for Qatar to US will deliver a bit less than designed.