Hi,
I would suggest that both your issues sound like algae issues. The hairy stuff could be black beard algae. Check out this website for identification and possible causes and remedies.
http://www.theplantedtank.co.uk/
Look under the plant problem tab at the algae guide.
Personally I'd agree with Bob in that the surface scum should be sorted out with a lot more surface agitation but I'd tackle the Black Beard Algae differently if indeed that is what it is.
Firstly I'd clean the filters out thoroughly (obviously in tank water) and all the pipework. Thoroughly clean the inside of the tank as well including siphoning all the detrius from the substrate.
Reduce feeding to a minimum.
What you are trying to achieve here is a serious reduction in the ammount of ammonia in the water column. Algae doesn't need much to flourish and despite your test kits telling you that it'll be zero there will always be a residual amount left, enough to trigger algae to bloom that's for sure.
Once you have reduced this to a minimum do a series of large water changes over the course of a couple of weeks. I have done 50% every other day for 2 weeks in the past with no ill effects when battling BBA. Keep your lights off and the tank shrouded from direct sunlight. You could use a product called flourish excel which BBA doesn't like at all but which is fish safe if you can afford it. I'd double dose with this as well.
BBA can be a nightmare to clear and you may need to blackout your tank completely for up to 4 days to starve it of light. Once clear its best to keep your tank hygiene up and maybe even add specific fish which eat BBA of which there are a few inexpensive peaceful ones to choose from.
Chris.