Do I need fertilizer?

I can help you out here...how many watts you have going there and what type of bulbs? The amount of fertilizer that the plants need changes depending on how much light they are getting. But if you are running a low light setup you could probably go without ferts except for maybe a weekly dosing of seachem excel. What species of plants do you have exactly?

First thing, is that either close ups of the plants, or names of the plants will be more important than the fish. Next, fertilzers are something you have to watch for. If plants start growing very slow, turning yellow or brown, die off, or you have excessive algae growth, you can bet that nutrients have something to do with it. Right now I'd say you don't have nearly the number of plants to need ferts. The best way to tell on many of the basics, is to test the water saturation of many of these nutrients. Nitrate being the main one to test for.

It looks like you have an anubias species on the far left with vallisneria sp. I can't tell what the other plant is.

the more plants the better. fish dont make everything the plants need but some lower light plants can do fine without.