You look to be in that final "stubborn" stage after the nitrite spike is over, ammonia is being processed down to zero in 12 hours and nitrite is being processed down near zero (1.0 in your case) and it just seems to stick there, without going to zero. We see this a lot and all and all its a good sign that you are near the end and should be finalizing your stocking plans, which can be quite complicated if you haven't tackled that yet. (# of fish tank can allow, minimum size of schools for various species, compatibility of species with each other)
I can't figure out what your tiny soft white particles might be. That doesn't ring a bell for anything I can think of. Only remote possibility might be that you are seeing bits of "biofilm" which is a film coating that gets on everything all over the aquarium from different species of bacteria (mostly (well, more) heterotrophs out in the tank, unlike the autotrophs we are growing in the filter) ... the biofilms are mostly clear but eventually get other stuff stuck to them and appear whitish on the edges. Usually they are described as little sheets of film pulling up on a surface, however, not evenly sand sized flecks like you are describing. Yours sounds more like something that might have come off the substrate or decorations or from a filter media or perhaps there was something strange in your ammonia (but obviously your ammonia is effective, as you are having a very fast fishless cycle!)
~~waterdrop~~