Whether 99.x% pure alcohol is important or necessary has a lot to do with what's on the part you'd clean. Depending on method it isn't very important. If your assembly order leaves off certain parts like pots and non-sealed trimmers until after cleaning, you can use lesser % alcohol.
As already mentioned, having a haze is usually just a sign it wasn't rinsed, or rinsed enough. Even with nearly pure alcohol I like to leave some parts off so it is no problem rinsing, even immersing parts. Sometimes when working with aged gear as with repairs, I find it helpful to put a bit of detergent on a toothbrush (or paintbrush for hard to access areas) to clean up other areas, then I rinse that with water (when the populated parts allow for this) then shake off excess and a final rinse with alcohol.
You could of course use only alcohol but I find water cheaper and more abundant. In a pinch I've also used water for final rinse and never had a problem doing so, but when I do that I shake off excess and leave parts drying for a day or more.
Whether flux can be left on depends on factors like how active it is, where it is, and depending on the flux, how humid the environment. Generally speaking the more active the flux the more important to remove it. Taking a popular brand and type, Kester 44 should be removed, ideally, though you're in no rush to do it right after soldering or even the same day like you would if using the wrong solder or flux (with acid in it).
More gentle fluxes like RMA or no-clean can usually be left on without issue, and they are harder to clean off. RMA gets harder but can still be removed with alcohol while no-clean should only be used if you will leave it on (but it's virtually clear, if you are THAT picky about your solder joints it may be more of a vanity issue than audio electronics issue).
Leaving on some fluxes will erode the metal a little depending on how active they are and how fluid they remain. Fairly active rosin fluxes are hygroscopic and the longer they sit, the more moisture absorbed from the air, the more gummy they become. At some point if it becomes too gummy, fluid, and thus more active, it can become more conductive. Many people never have the problem later if they didn't clean it off but it is possible.
