So I'm gearing up to play my first tournament in a few weeks, my first games in fact so trial by fire it seems.

I have had a look but can't seem to find an answer to what I'm sure are a couple of very basic questions about Strict Orders.

Does the effect work beyond range 3 of the commander that Strict Orders is on? I'm not 100% sure on what is and what is not affected by the command range so best to check

Does the effect work if the commander that has Strict orders is on is not the chosen commander for the turn? i.e. a Separatist Army with both Grievous and Dooku in it, with Dooku having the Strict Orders upgrade but Grievous being the chosen commander for the turn.

Your questions are kind of linked, so to answer them both: Strict Orders places no limitation on who issued those orders, and no range limitations, either.

Strict Orders does not have to be on the commander who issued orders during the command phase. The card does not specify who gives the orders, just as long as the trooper unit has a faceup order token (i.e. was issued an order during the command phase by some effect). The trooper unit does not have to be within the command range, as you could have 2 commanders, one who issued an order to a trooper within range 3 via a command card, and another commander equipped with Strict Orders, who may be beyond range 3 of those troopers.