the white filaments might be anchor roots. Anacharis will send long whitish trailer anchors to hold itself to the substrate or anything else it can get ahold of. If it is whispy whitish stuff it is something else.
Brown/ yellow / transparent melting look on the anacharis could be degradation of the leaves (nutrient deficiency like iron, nitrogen or even light). Maybe let it float at the surface to see if more light helps.
Brown granules on there could be diatoms, an organism that brushes off somewhat easily. Common in newer tanks, but seems to go away with time and water changes. Completely harmless.
Brown tough to remove algae is also a possibility (Red Algae I think it's called) A sign that you have plenty of one nutrient, but lacking the others.
more info like size and age of tank, inhabitants, type and wattage of lighting, how often you feed, water change habits, etc would all help us to help you.