White doesn't sound like algae to me. It sounds like some kind of film or buildup (probably not anything toxic like a fungus unless it grows on your fish too, but I couldn't say for sure). Mostly the "fan" structure is probably just aquarium scum or an odd kind of algae I have never heard of, and yeah, it could just be wiped off. People seem to think that algae in a tank is a bad thing, but a huge portion of the oxygen on our oceans is created by photosynthesizing algae, so it will perform the same functions in your tank. But I understand that visible algae can be annoying. If you MUST get rid of it, I would definitely not recommend algaecides or other chemicals to get rid of it. I don't know for sure if they could hurt your plants but I wouldn't risk it, and I personally try to refrain from adding any chemicals to my tank. Good luck!