In rough order:
Here is a heads-up features comparison of the Gigabyte boards: Newegg Comparison
Unless you're running multiple graphics cards and/or doing heavy overclocking you can probably skimp a little on the motherboard.
Yes the components you've chosen (MB/CPU/RAM) are all compatible.
However, I don't know if your other components are (hard drive/optical drive)
If you open your case you should see a sticker on the power supply that will tell you the Watts and Amps on the 12v rail(s).
While your case is open look for a flat grey ribbon going from the motherboard to either your hard drive or optical drive.
If you're having troubles with it snap some pictures and post them up.
Please read through the thread thoroughly before responding.
Nobody wants to read a wall of text, formatting is your friend.
i5 3570k | 8GB G.Skill 1600MHz | R9 290 | SeaSonic 750X