Are your orders clear?" the commander asked
"Get 'em up, get 'em up, get 'em up!" she shouted to the pilot, as the soldiers boarded the transport aircraft.
the unit's soldiers shouted smartly back.
Use context to describe how the characters respond, rather than adverbs. It's understood (to me personally as a reader) that the soldiers are a.) intelligent, and b.) spirited, and c.) neat. (Three definitions of "smartly", according to Merriam-Webster.) Since they are shocked at the fact that someone important is taken, they will be more willing to go ahead on this mission than if it was just a simple "storm the base!" mission. So they will respond to their orders in a spirited manner.
The "furiously" to describe how the helicopter's blades are rotating isn't needed. The helicopter is prepared to take off. Of course its blades are going to be going that fast.
The tall, brown-haired squad commander
I don't know the rest of the context, so I won't comment on whether it's appropriate to describe the character in this one scene or not. But I will say that you shouldn't come out with the description like that. Integrate it into the narration so you don't smack the reader with it.
example said:
A lock of her brown hair escaped from her military cap. She tucked it underneath while still explaining the mission.
This way, the physical description blends in with the narration. It doesn't stand out, disrupting the flow.
Just from a quick read-through of the scene, and without the context for the rest of the fic, I can't say much else. Just remember that this is what I personally see wrong with it, and aside from the grammar, you should always wait to see what other people say, and weigh what they say with what you know of your story, and respond accordingly.