i would imagine the water could have whatever you want in it so long as it isnt affecting the life in the tank negatively... the particles you see floating are probably leftovers from breakfast and what comes out after breakfast... those particles will cause ammonia to rise in the tank which will damage your poor little fishes' gills and they will die... but i see many amazon styled tanks which seem to have a gloominess to them but i imagine that its to mimic the real habitat.. so all i can say or anyone else can say for that matter is make sure you are testing your water regularly to monitor your ammonia, nitrites, and nitrates. so when they say "MAKE SURE THAT DARN TANK IS CLEAN!" you don't necessarily need to have crystal clear water. So I say just dedicate a little time to the tank and stay on top of the testing of the water parameters and if you go without troubles that means your water is clean. Remember you dont have to be able to drink the water for the fish to love their environment.
indeed.
when you hear about keeping your water "clean", generally its a reference to water parameters, more so that visually clean (though the two are somewhat connected). as long as you have proper biological filtration, and you are keeping up with routine water change to maintain nitrate levels, your tank will be "clean".
water polishing (removing fine particles) is a whole different monster. filter floss, quilt batting, poly fill, micron filters, etc, all p[provide good means of polishing, but you still need an effective delivery system. you cany just add the media to your sump/HOB/canister and expect it to work. if the particles never make it to the intake of your filter, they cant be removed. generally this is where water circulation comes into play.
there are many aspects to "clean" water. but again, as long as your water parameters are in order, your fish will be happy.
some of my tanks have brown/ tea colored water, but i assure you, the water is as clean as it gets.