Wow, those are some huge photos. Not much doubt in my mind that's cyanobacteria. (all due respect to Willow...)
Much has been written. WetWebMedia.com is as good a place as any to begin. Short course: skim wet, feed less, change water, increase water flow. The tank is pretty new, so you may be getting a lot of nutrients into the water from the LR. I'm also a bit suspicious that your phosphate test is faulty, as 0.0 in tapwater seems a tad unlikely.
I'm no anemone expert (but I can culture aiptasia without trying). Looks a little like a codylactis - which is an Atlantic. Others will chime in, I'm sure. If it is, there's not much chance your clowns will accept it, and if they do, no guarantee the anemone won't eat them. Before I got my anemone (bubble tip), I did a bit of reading, and discovered that: a) not all clowns will host an anemone in captivity, sometimes preferring a powerhead or mushroom or soft coral; and b) various species of clowns have distinct preferences about anemones. ReefCentral has a good faq:
http://www.reefcentral.com/forums/sh...hreadid=282136
Matthew