Is this the correct SATA cable?
Yes that is the correct cable that plugs into the motherboard SATA ports. Regarding the power cable. Some SATA drives have both the old style 4-pin power connector (like on the IDE drives) as well as the newer SATA power cable. If it has both, DO NOT plug both in at the same time or it can damage your PC. You can use one or the other but not both.
Yes. You will also need to power the SATA drive, so if your power supply doesn/t have the right connectors it, you will need an adapter.