It sounds like it is one of the plant grow bulbs.
Running 2 of the bulbs will not require CO2 dosing.
Eco-complete is a good start. A picture of the "mystery plant" may help determine further requirements. With anubias and java fern, you probably won't see a need for root tabs or much fert (especially with the eco-complete). I would recommend you look at dosing a trace mix once you get a new fixture. Flourish trace is a good one.
The bulb you have now might be sufficient... are you noticing problems with the anubias and java fern? They don't require much light to survive. If you plan to add additional plants that might have higher lighting requirements, then a single bulb may be insufficient.
Can you look on the bulb and check the wattage? Also look for the color temp if it is on there. If it is pink, it is probably one of the ~6500K plant gro bulbs, but it would be good to know for sure.
Here is some good info on fertilizer, just so you have a better understanding of it:
Plants need 5 big things to grow, and several smaller amounts of other nutrients to thrive.
The big things:
1. Light
2. Carbon - This comes in a few forms... your plants will use CO2 in the water to get this. Without injecting CO2 your water will remain at equilibrium with the air, around 7ppm CO2. By injecting CO2 (pressurized, not DIY on a tank of your size) you can raise the CO2 to "unnatural" levels and essentially kick the plants into high gear. The consensus is the most beneficial level is somewhere between 20-40ppm CO2. You can also add Carbon by using a product called "seachem excel". It works very well with most plants, but can cause problems with others (namely hornwort, anacharis, and a few others) so read up on it before putting it in your tank.
3. Nitrogen (N): One of the 3 "macro-nutrients" for plant growth. If you have fish in your tank, there is a natural source of N provided by fish waste and uneaten food, in the form of ammonia, nitrite, and nitrates. Your plants will soak up these forms of N and use them to grow. As you add more light to a tank, especially if it is heavily planted, your plants may use up all of the N in your tank, and it may become necessary to supplement the N using fertilizer.
4. Phosphorus (P): the 2d of the 3 macro-nutrients. It occurs naturally in many water sources, and is also found in many foods and other organic material. It may be necessary to dose P in high light tanks where the plants are using up all available naturally occurring P. It occurs in the tank in the form of Phosphate, PO4... so you can get a phosphate test kit to check how much P your plants have available to use.
5. Potassium (K): The last of the 3 macro-nutrients. K doesn't occur naturally in much that is already in a standard tank. Most off the shelf aquarium fertilizers contain K (and not the other 2 macros). It is less harmful in large quantities, and almost any tank (from low to high) will benefit from the addition of a supplement that contains K.
The micro-nutrient or trace elements:
Plants also need other nutrients in much smaller quantities that are often referred to as micro-nutrients or trace elements. These include Iron (Fe), the most common trace element added, and a commonly available fertilizer. It also includes other elements, like Boron, Mg, Cu, Ca, etc.
Most ferts you find in your local fish store will be a liquid form that combines 1 or more of the nutrients I described above. Most serious FW Planted tank hobbyists prefer to dose each of the 4 categories above individually using dry fertilizers. The liquid ferts sold in LFSs are very expensive in comparison, sometimes costing 20-70 times as much if you add up what you are getting per dose.
In addition to liquid dosing or dry dosing to the water column, there are also "root tabs" available that get "planted" in the substrate under the plants. They can do wonders for plants that are heavy root feeders. They contain 1 or more of the categories of ferts (N, P, K, or trace) I described above. With your substrate, they probably are not necessary.
