I wouldn't install anything 'permanent' on the floor in the basement. The house will continue to settle. Consider laying an 'area' type of carpet or rug. Use furniture 'strategically placed' in the room to keep it from moving.
RE: Fixing the cracks - If you have a Warranty, I'd wait a while. It's possible that the cracks will continue to grow, even slightly. Just make a note and contact the Builder as you near the end of the Warranty. Be SURE to notify him of you via register mail return receipt.