Do you have a water test kit? That is the easiest way to check your water quaility, especially since you have been having mini-cyles. Cloudy water can be many things, but if it looks like someone poured milk into your tank, that is totally harmless and will clear up within a week.
To help improve the quality of the water, the easiest way is to do frequent water changes. I have gone through times when I had to do daily water change. Make sure you are using dechlorinator, and adding salt can also help.
For the fin-rot, does it look like the edges of the fins are eroding away? Can you describe the white stuff a little better? Does it look like little bits of cotton are growning on the fins?