No, algae is not killing your plants. Your plants aren't growing, that is the problem. When I started a planted tank way back when I had loads of algae but the plants grew fast enough that I didn't mind much. Some of your plants look fine, they seem to like your tank - if they have been in the tank for a while. Some look horrible, guessing they aren't happy with the situation. Replacing plants that are actually dying with more of the happy plants plus some fast growing stems and/or floaters might help your tank.
Has the hairgrass done anything at all? I'd check for healthy runners and cut back the top growth of what you have if you can without uprooting it if there are runners. Right now it is a handy substrate for that algae which is probably enjoying the nutrients leaking from the dead leaves.
How about reading through this synopsis of Tom Barr's low tech system to see if you can figure out what the problem is? http://www.sudeepmandal.com/hobbies/...ed-tank-guide/
I don't know anything about your lighting but it should be on a timer for about 8 hours a day. Perhaps lighting is too strong, put a layer of window screen down between tank and light or raise the fixture and see if your plants grow better or use only one fixture. According to this link the Marineland LED would add about 25 PAR to the other light, that is quite a bit for a non CO2 tank. http://www.jlaquatics.com/product/ld...7+Inch%29.html
and the Fluval, this shows PAR for salt water fixture but the fresh water is likely not much lower in PAR http://www.reefs.com/blog/2012/07/12...sea-led-light/
The goo covering the hairgrass might be cyanobacteria which can show up when there is very little nitrate available. If the green is hard to scrub off it might be green spot algae which can show up when phosphate is low and plants will always need more potassium and micronutrients than fish poo/pee or root tabs provide.
I know algae eaters aren't the solution but they help keep plants cleaned up just because they go over all the tank surfaces constantly. What do you have in this tank? I have platies, ramshorn snails, otos and a couple bristlenose plecos.