I understand your lack of space, I live in a single college dorm room so it's only a little bit bigger than a walk in closet. There is no way I can fit anything larger than what can sit on my windowsill since I have a ton of other stuff in my room. I am fairly certain my two gallon fish bowl is more than 2 gallons since it holds more water than the 2 gallon rectangular fish tank I had. It's 10" x 10" x 7".
Definitely get a light bulb for the plants even if they're supposedly hardy. I got a anubias plant for my tank and it started dying. My friend has a full spectrum bulb she attaches to her desk lamp and her plants seem to be sprouting like crazy.