are you able to fish at the Bruneau Dunes ?

I did not fish, I was but traveling the state. Fishing is allowed and hear it's great for bass and panfish.

When I was there 5/3/21 hiking the loop around both lakes, I could see many fish jumping on the surface at dusk. Unfortunately, I didn't have any fishing gear with me so I was left kicking myself for not keeping it in the car.

Yes, fishing is allowed. You can find Largemouth Bass, Bluegill, and some holdover Rainbow Trout that we aren't sure will survive the summer heat (in the Big Lake)

Yes

Bass in both lakes, perfect habitat around the shore.

Yes... but not sure what type of fish are in the lake.