cleaning the engine, and keeping it clean-how do I?

To answer just your question, you can just get a wet rag and wipe the engine clean. It may take you 15-30 minutes but it's the safest way to get the dust out of the engine compartment.

 

Most of the dust seams to enter through the front grill and radiators. The seal across the hood and the plastic rad cover also play a part in this.
The bottom covers appear to be more to do with airflow under the car.
One thing I would make sure of if there was front end damage is does the AC work and do the radiator fans blow towards the engine from the front grill, and not in the reverse blowing out of the grill. This is not at all uncommon with front end repairs. The problem being the two fans rotate in opposite directions, and if the blades are replaced on the wrong side of the car they blow in the wrong direction. This usually shows up as a high external air temperature on the MFD with the AC on, and the AC getting warm at 40 to 50 MPH. This will also draw dust up from the road surface acting like a vacuum cleaner.

John (Britprius)

 

There's a thread going right now about an AC compressor connection that's corroded right out, will likely necessitate compressor replacement. That's one reason to not use water. Anyway:

I'll vacuum what I can reach with a wet-dry, then switch it to blow. A leaf blower, or some source of compressed air is also good. An old paint brush will help. Also one of those duster on a stick: you can run it in between components.

 

That and if the bottom cover is missing below the condenser the ac condenser will take a real beating from road debris. It gets kicked right into the condenser which sits in front of the radiator. New condenser could be $1500 installed.

 

The display on the center of the dash is called the MFD (multi function display), and it displays outside air temperature actually from just inside the front grill. When the fans are reversed they blow warm air from the rads over the sensor giving a false high temperature reading.

John (Britprius)

 

Another variation is an old paint brush to loosen dirt/various residues, a spray bottle (with only warm water or very diluted Formula 409 for degreasing) and rags to wipe.

Here in dense city life, it's a losing battle. The darn thing collects dust with dedicated regularity!

Dealer has special offer of $199- to steam clean

 

I cleaned my engine/engine bay using Purple Power in a spray bottle and rinsing with a light pressure hose. I did stay away from the inverter and all Orange wires. It was very dirty and it looked near showroom new when complete.

 

To each his own, but I'd avoid spraying the engine bay. Water can get into connectors, with expensive outcomes. See post #30:

Corroded AC wiring harness 2010 - anyone heard of this? | Page 2 | PriusChat