As far a fertilizing, without light to photosynthesize, the plants wont use much added fert. If you believe you need fert, I would suggest a simple LFS brand, as you wont need much. They say like 20ml every week, so the bottle only lasts a few weeks, and youve spent 7 dollars on it.
You should focus on your lighting first. Make the tank look a lot more visually pleasing, and help your plants at the same time.
Once you upgrade lights though, you are gonna wanna do the big three upgrade at the same time... Its a hand in hand package.
1. lights
2. CO2
3. fert
2. and 3. are easy; DIY co2, and plenty of fish.
Or you can focus on your lights and start using the nutrients in the column currently.
Dont plan on this working on larger tanks, without pressurized CO2, and EI ferts.
BTW, clear stringy leaves are considered "melted"; Terminology lesson...