The plant is pothos ivy and you can get it at any home improvement store. (home depot, walmart, lowes, etc) This plant is ideal because it grows well in water and it requires almost no light. It will thrive in any room as long as there's a window in it. It is an indoors plant.
Ideally you should take a few cuttings and put them in the tank, within a week they will start developing roots and after that they will thrive. As you can see in the pictures I posted I only placed a small bunch with a few leaves in the tank and it became a huge plant.
Make sure to remove any leaves from the bottom so you can submerge a few inches of the stalk in the water where the roots will develop (you will see little brown bumps in the stalk of the plant around the leaves... that's where the roots will come from so make sure at least one of them ends up submerged). Any leaves that remain submerged will eventually rot and pollute your tank.
I used cuttings because removing the dirt and soil from the mother plant can be a pain in the ass. and some people have reported that they don't do as well when transferred from soil to water... so use cuttings instead. Also that way you always have a supply of cuttings from the mother plant in case something happens to the one in your tank.
Fish won't nibble on the roots and if they do, it's harmless. I have never had a problem with it.
another tip is to take out the plant every now and then and rinse the roots with tap water... they can accumulate debris over time and that slows down the nutrient absorption from the water.