Here's a few answers:
1. The box that was crushed is the resonator chamber for the airbox. I'd replace it, or at worst, seal it up with some duct tape until the weather breaks.
2. Direct wire 12V to the fans to see if they come on, or if they are damaged. From there, we can diagnose the issue, which may be cured by #3 below.
3. Your idle is jumping because your coolant is low. The coolant temp sensor lets the ECM know when to kick the car out of high idle, and if it can't read anything, it goes into a feedback loop, resulting in a BRUM BRUM BRUM BRUM type choppy idle.
With the engine cold and the car shut off, remove the radiator cap and inspect (the overflow tank will not tell you the level in the system). Fill, and start the car, allowing air bubbles to rise to the surface for a minute or two, and reinstall the radiator cap with the engine running. This should cure the choppy idle.
Tim Poliniak - ASE Certified Parts Specialist, 19 years with Acura/Honda
Acura of Peoria ~ www.oemacuraparts.com