You don't need to feed it, it will catch what's needed on it's own but do not close it's traps on purpose without anything in it because it is bad for the plant and each trap can only close 3 times (I think it is 3 if my memory is right) before it dies, so do not waste them with nothing in them and yes I know people love to watch them close when they see one lol.
It is a plant so what it needs is sunlight so sit it in a window sill that gets almost full to full light. Mine is facing southwest-west. This is probably the most important part! Proper sunlight is key because it is how the plant makes it's energy through photosynthesis.
Plants also need water so put water in a dish just like you did and let the fly trap sit in it. Do not pour water directly on the plant though as they will get all the water need from the dish, just make sure it is always deep enough to cover the roots. Also do not use tap water that has chlorine and other chemicals in it. I use spring water for mine and you can buy that at Wal-Mart for like 87 cents a gallon or something like that.
Lastly that small pot is big enough for the plant as it is only 1 plant. The seperste traps are not seperate plants but in fact are the "leaves" of the plant. They will die and also new ones will grow but the plant is only one plant and as a whole will still be doing good if a few traps die. What you should do is snip off the dead ones or "old gorwth" so that the plant can focus it's nutrients and water and energy to the baby traps or "new growth".
So in summary, do not need to feed (but I know it is cool to watch), keep them in sunlight, water with spring water in a dish, and cut the old growth. That's about all you need for a healthy plant, pretty simple right? lol.
I hope this info helps and if you have any questions feel free to ask.
Good luck and good growing!