Two questions - is the idea that the nuts will be strained out? and if i make it in advance, do i bring to room temp or leave chilled? thanks!

So it doesn't specifically say to strain the pistachios but is that what is meant by straining, in addition to straining out any cooked egg bits? Are the nuts to be tossed? Seems a shame as pistachios are quite expensive. I imagine the texture might be confusing with the nuts in the custard but that's a lot of pistachios to just throw away.

Also I love a crème brûlée to be cold and creamy with a shattering almost burnt sugar crust.

I suspect the nuts are meant to be strained out, so they just infuse their flavor into the mix w/o adding potentially off-putting texture. Rose Levy Berenbaum has a pistachio creme anglaise recipe in the Cake Bible that does the same thing and it is delicious, and tastes obviously of pistachio.

No, the nuts are incorporated in the custard, no straining is indicated in the recipe. Besides the nuts are finely chopped.

Keep in the fridge until you are ready to glaze and serve promptly. That's what restaurant pastry kitchens do.