...from common observation, I can easily conclude there is a lot of infrared (from burning, superheated fuel), ending somewhere near yellow of visible spectrum; there should be next to none of UV and higher. But how far up does it reach? Do the engines emit a considerable amount of microwaves?
This question is motivated by "How does a Falcon 9 booster know how far away the ground is?", and relevant available options.
The obvious solution is "reflected waves", but they must be in a spectrum not obscured by the engines. Ultrasound, or anything audio is right off, with the enormous level of audible noise. A laser (visible or IR) distance measurement will have the dot lost in the bright flame. I wonder how viable microwaves are, though - essentially, a radar.
For example, during a spacecraft reentry, the communicational blackout is caused by the plasma of superheated air and ablator, radiating on a spectrum broad enough to flood both long waves and x-rays with enough noisy energy to make them not viable for communication. Rocket exhaust is much less energetic, but it's still one of most energetic large-scale emissions achieved by technology and I wouldn't be surprised if it exceeds the standard "visible+infrared" range of "burning stuff".