EP2C20Q240C8N and giga ethernet

The GMII and RGMII interfaces don't use LVDS. They are single ended and use much lower frequencies on a parrallel bus: 125MBps/pin for GMII and 250MBps/pin (DDR) for RGMII. But those interfaces use a lot of pins, so you should check that you have enough pins for your application.

Your second question can't be answered, it depends a lot on your design. You should compile it in Quartus and use Timequest to check that your timing requirements can be met with your design and the device that you selected.