Let's go over this one step at a time - But first of WELCOME TO THE FORUM
Often certain fish are bought in hopes to battle algae, most people incl the Sale rep at the fish store don't know that certain fish only eat certain algae or non at all. That's the problem you're facing. So my suggestion, trade him in for plants at your LFS.
Secondly adding chemicals to a tank who's obviously out of balance which is why you're having algae to begin with is really not a good idea. It will temporarily mask the issue, but in the long run, assuming you want to keep a nice planted tank for yrs to come, its much more advisable to eliminate what is causing your algae. That said to better assist you there: What does the algae look like, green slim? dark green brownish lil bushes? Green Hair strings? Describe it the best you can and/ or take a picture for us.
I just recently had a terrible outbreak in my 55g with 4-5 different types and battled it successfully, so there is hope.
For plants: No you do not need CO2, the stock you have will do just fine. For good plants growth you need TWO things and they need to be balanced 1) Light 2) Fertilizer. The lights you currently have will work for some plants (low light as you realized already) add some comprehensive all in one liquid fertilizer tot he water as well (available in your LFS).
How are your Anubias
planted? Often people burry them in the gravel which hinders their growth as they ideally should be planted attached to either a rock or driftwood. That's also the same way to plant Java ferns.
Now bulbs should ideally be replaced 1x year. So when your time is up for your current bulbs, replace it with a daylight bulb. These are rated at 6500K and are the spectrum plants need for successful growth. You can either buy these at the LFS for about $15-20 or you go to Lowes, Homedepot, Walmart and pick one up that's named Daylight (available by Phillips, GE, Bright Effects and Lows knock off brand) and you spent $3 for 2x4ft bulbs
Same thing, same effect on plants but cheaper. Feel free to check out my tanks to the left under the tap "Aquariums" and look at the plants there, all these are set up with the very names homestore bulbs and no fert's and see for yourself how that works for me.
Planted tanks are often set up TOO COMPLICATED meaning too much "messing with nature" less is more and all it needs for a nicely planted tank is BALANCE between lights & fert's & fish
FYI since you mention Iron, plants need far more then only Iron, they also need trace elements and micro nutrition, which is why I suggested the comprehensive liquid fert above already