So I spent some time phone tagging between Qantas Premier and Chubb insurance and worked out the answers:
* Taxes associated with an award booking payed for on the Qantas site using the Premier card qualify for the bonus point/$.
* To trigger the travel insurance when using points to make an award booking the points used must be from the Premier card. I don't know how they check that, but if you use 200k points and only have earned 100k points from this card, I guess that would not qualify. Basically the total cost of the flights must have been payed with the Premier card. The cash component is easy, but they also require any points component to be from points earned from the card. I am not sure how they check that, but it seems to me that it would be difficult to prove you have activated the insurance if doing flights using award points.
In my case, if I use the Amex card to pay the taxes, I get more points (2.5 vs 2 per dollar spent), and the Amex purchase will also activate the qantas lounge passes on that card (where the premier card lounge passes are activated on anniversary with no qantas spend). The qantas premier insurance seems better than Amex (it covers global hire car excess and has more cover for most things), but I cannot be sure I will have activated it as I will be using more points to make the booking than I have earned from this card.