I am not sure... it does look like something I have seen on the mother in laws tank before. They where told to shorten their light cycle for a while and to cut back on how much food they give.
I can't say one way or another on whether that worked or not though.
What is the texture of it? If that were in a SW tank, I'd say it's cyano...which is possible in a FW setup but it's usually not red, blue-green is more common. Does it rinse off?
A form of bba I believe. Go to Google Images and put in black beard/brush algae. And then when you research it you will find it is a PITA to get rid of. SAEs will eat it but only if they are very hungry. I once collected all 7 of mine from various tanks to fight it in my high tech 50 gal. If you look closely you can see the tufts of bba in the hairgrass.
Yep. BBA. Generally once it starts on moss its really difficult to get rid of. SAE's really don't get rid of it they just tend to mow it like grass. This greatly slows the spread of it in the tank. It still hangs around forever though.