I would think that fuzz may be his slime coat from the medications which is his natural defense against parasites.
About decorations i would wash them and just keep them out of the tank until you know he don't have parasites any longer. If you have live plants take them out and quarantine them in the water without water conditioner untill you know he don't have parasites any longer.
Take the filter out.
Do you still using medications? If you finished them or if you will finish them soon i would start him on aquarium salt 3tsp/gall with daily 100% water changes.
When you do 100% water changes make sure you acclimate him. People do it diffirent ways. You can have him in his changing cup with about 15% of the water and keep adding new pre mixed water about every 5 min for about 4-5 times. This way he will get used to the new water temperature . There is a few other methods to acclimate betta to the new water temp/chemistry. I think it a bad method when you put betta in the bad and let it float for some period of time ...I am not sure how to do it, may be other people will give you instructions.
Of course you need to add salt with each water change when you do 100% water changes. You can pre mix in in one gall jug and use it for 2 treatments. Always cover the container when you acclimate him to prevent him to jump out. They really good jumpers. My bettas always try to jump out when i keep them in their changing cup.