I am an undergraduate sophomore but I will be able to finish and graduate at least a semester and maybe a year early if I take the classes I need to get my BS. Either way I will have space in my schedule (I had a lot of credit coming in from high school) However, I have a scholarship and I would like to stay in school for the full 4 years. I plan on attending graduate school. Can I take graduate classes as an undergraduate and have them transfer to graduate school? What should I so with the extra space in my schedule to be productive or to help me get into graduate school?
It really depends on where you go for graduate school. Some schools may accept graduate courses from other places, some will allow you to use them to test out of prerequisites, some won't accept them at all.
That being said, taking gradate courses as a undergrad will look good on your gradate school applications. Depending upon your subject, if you can also manage to swing some undergrad research experience, your gradate school applications will be in really good shape.