Java fern leaves get nasty looking as they age. You trim off the old, encourage the new.
I assume those ferns aren't buried? They do best tied (or super glued) to wood. Tied to a rock will work OK too, but they need to be exposed to water! If they are sitting UNDER those rocks that's part of the problem (it looks like they might be.)
1. Replace the light. Don't over do it, but get a light that will put you in solid low/medium light range. Get a timer and give it a 8 hour photo period to start. This will mean you never forget to turn it off or on. Consistent light is important.
2. I'd suggest looking into dosing weekly with a general fertilizer like Seachem Flourish. Don't over do it or you'll have algae, but give your plants something to work with. You have one fish in there it isn't creating a lot of waste for the bacteria to process or for the plants to use. So supplement. You don't have to get fancy, you don't need CO2, but a little fert wouldn't hurt.
Frankly I'd try tying that moss to a piece of wood, tie the java fern to it as well and then leave it alone for a couple months. I'm guessing it will start to grow with a little fertilizer and a better light. Moss through mesh will take a long time, at least that's what I've seen. And some varieties of moss just don't grow quickly.