As a building material carbon could conceivably be used for everything on the space station, because carbon is such a versatile material.
Carbon fibres are already used to make very strong and lightweight structures, and the basic structural spine of the station could be built this way (I am going to assume an ISS like structure, but with suitable tweaking you could build to the shape you like). Carbon finer can also be woven into cloth, so inflatable habitat modules such as the ones being pioneered by Bigelow Aerospace are possible. So we have the basic structures.
More advanced carbon materials like Graphine or carbon nanotubes have been demonstrated as energy conversion devices, making the basis for solar cells and superconducting "cables" to move electrical energy around. Computers, communications devices and other electronics can also be made from various forms of Graphine and carbon nanotubes. A bit of "cheating" may be needed in the form of "doping" the materials with small amounts of other elements. These materials may also be used for more mundane purposes like making pipes for plumbing roll the graphite sheets into a tube). Graphine may also be used to make high efficiency filters, making a graphite sheet with molecular sized holes just large enough to pass the molecules you want can be used to separate pure water from contaminants, or keep CO2 on one side of the barrier for the air purification system. A form of carbon called Bukministerfullerine (C60) has 60 carbon atoms arranged like a soccer ball, and can theoretically be used to store gasses like Hydrogen inside the molecular matrix, which might be useful for the astronauts.
Mechanical parts will need to move, so carbon in the form of Graphite may be needed to form sliding and rotating interfaces and bearing surfaces for your space station.
A few things will need to be kept in mind. Most forms of carbon described have very high tensile strength, so the comparisons to earthly construction is balloons and tents, rather than the Eiffel tower or Great Pyramid. For high compressive strength, you will need to go to the expense of changing the carbon into diamond, which is also extremely good as a heat conductor and can also be used as the basis of semiconductor materials as well.
Your space station will be possible, but you will need to take some fairly impressive machinery to mine the carbon materials and then process the carbon into its various forms to make building materials. You should also keep the need for other elements to "dope" various carbon materials to change electrical and other physical properties if you want to make solar energy systems, cables and comms wire or have the carbon take on other properties. In the long run, a colony on the asteroid itself will become wealthy by setting up the industrial plant needed to mine and process carbon into the various forms useful for various projects.
