Your motherboard will (should) come with a few SATA cables. Take a look at yours specifically and it should list box contents somewhere. I'm assuming the power supply you chose will have SATA power, as most do nowadays, but you could check to make sure.
Anti Static wrist straps can't hurt for the money. You should be fine one a wooden table with no carpet under your feet (no socks imo either) and touching the case before touching any piece of hardware.
But for a few dollars a wrist strap is better safe then sorry.
Yes, better safe than sorry. I use an anti-static wrist strap when I build.
Some mobos come with as many as 4 SATA cables, others may have only 1. If you either can't tell or know you won't have enough, you should be able to pick up extra ones for $3-$4 each. Modern, quality PSUs have SATA power connectors on them. Choose one from Antec, PC Power & Cooling, Corsair, or Seasonic for good results.