The "hair" is probably black hair algea which is very difficult to get rid of once established in a tank, it is generally caused by high nitrates, phosphates in the tapwater and excessive ligting times but also thrives in tanks with a lot of surface movement. My personal advise is to pull out all the plants and replace them but if that is a bit extreem for you then you can try some or all of these methods.
Check nitrates, if they are above 10ppm then you need to do more/larger water changes, if your water source has a nitrate level higher than 10ppm you will need to use water from a alternative source like R/O water.
Reduce lighting times, planted tanks need 8 to 12 hours light a day so if you have your lights on for more than 8 hours cut them back to the minimum.
Add more fast growing plants to use up nitrates and phosphates quicker.
Add a CO2 unit to the tank to increase plant growth so nutrients are used up faster.
Use a phosphate adsorbing media such AP Phoszorb or Rowaphos.
Remove any airstones or air powered ornaments and push powerheads and filter returns below the waters surface to lessen surface movement.
The colour in neons fading is usually a indicator of neon tetra disease which in incurable and once present in a tank impossible to get rid of without complete sterilisation, watch out for fish not schooling with the rest and developing kinked spines, if you see these symptoms euthanise the fish immiedietly . NTD is found in most neons now due to bad captive breeding and poor conditions at far east fish farms so this is in no way a reflection on your fish keeping skills.
