My motherboard supports SATA 6GB/S. Should a hard drive also need to support 6GB/S for using it? Or a normal hard drive like seagate barracuda 1TB 7200 RPM will run @ 6GB/S?
To run at the full speed of 6 Gbps, you will need both a motherboard and a hard drive capable of that speed. It sounds like you have a 6 Gbps motherboard and so you would also need a hard drive that can run at 6 Gbps to run at the full speed. However, you can also install a "normal" 3 Gbps hard drive: it will just run at 3 Gbps instead of 6 Gbps.