Is my PC completely compatible?

That PSU is still a G1.

I changed up your build. Much better SSD for $10 more and a better PSU.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-7600K 3.8GHz Quad-Core Processor ($238.75 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.88 @ OutletPC)
Motherboard: MSI Z270-A PRO ATX LGA1151 Motherboard ($114.99 @ B&H)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2666 Memory ($94.99 @ Newegg)
Storage: PNY CS1311 240GB 2.5" Solid State Drive ($74.99 @ Best Buy)
Storage: Crucial MX300 275GB 2.5" Solid State Drive ($89.89 @ OutletPC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.33 @ OutletPC)
Video Card: MSI GeForce GTX 1070 8GB Video Card ($394.99 @ Newegg)
Case: NZXT S340 (Black/Red) ATX Mid Tower Case ($59.99 @ B&H)
Power Supply: SeaSonic 650W 80+ Gold Certified Semi-Modular ATX Power Supply ($69.99 @ Newegg)
Operating System: Microsoft Windows 10 Pro OEM 64-bit ($128.31 @ OutletPC)
Case Fan: Corsair CO-9050016-RLED 52.2 CFM 120mm Fan ($17.49 @ OutletPC)
Keyboard: Corsair Vengeance K70 Wired Gaming Keyboard ($129.99 @ Corsair)
Headphones: Kingston HyperX Cloud II 7.1 Channel Headset ($89.99 @ Jet)
Other: The Anchor - Under-Desk Headphone Stand Mount ($17.06 @ Amazon)
Total: $1605.63
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-02-24 10:45 EST-0500
 
Woops, did not take out your PNY SSD from the build.

Here:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-7600K 3.8GHz Quad-Core Processor ($238.75 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.88 @ OutletPC)
Motherboard: MSI Z270-A PRO ATX LGA1151 Motherboard ($114.99 @ B&H)
Memory: G.Skill Ripjaws V Series 16GB (2 x 8GB) DDR4-2666 Memory ($94.99 @ Newegg)
Storage: Crucial MX300 275GB 2.5" Solid State Drive ($89.89 @ OutletPC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.33 @ OutletPC)
Video Card: MSI GeForce GTX 1070 8GB Video Card ($394.99 @ Newegg)
Case: NZXT S340 (Black/Red) ATX Mid Tower Case ($59.99 @ B&H)
Power Supply: SeaSonic 650W 80+ Gold Certified Semi-Modular ATX Power Supply ($69.99 @ Newegg)
Operating System: Microsoft Windows 10 Pro OEM 64-bit ($128.31 @ OutletPC)
Case Fan: Corsair CO-9050016-RLED 52.2 CFM 120mm Fan ($17.49 @ OutletPC)
Keyboard: Corsair Vengeance K70 Wired Gaming Keyboard ($129.99 @ Corsair)
Headphones: Kingston HyperX Cloud II 7.1 Channel Headset ($89.99 @ Jet)
Other: The Anchor - Under-Desk Headphone Stand Mount ($17.06 @ Amazon)
Total: $1530.64
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-02-24 10:47 EST-0500
 
Solution

ThePCPicker24

Commendable
Feb 10, 2017
47
0
1,530


Thanks so much. Seems awesome.
Last thing, do I need any extra cables to connect my PC to internet and monitor or does it come with this?
 
Your computer parts will come with all cables needed to connect everying internally together (so inside the box) outside the computer it comes with nothing so you wil need cable for internet (some vendors label this correctly as cat5 or cat6 but most will just say "etherent" or "lan" cable on box).

EDITED: correciton, your PSU will come with a power cable, but the PC parts wont come with any other "external" cable

As far as video that completley varies form monitor to monitor, higher end ones will come wiht a cable of all types, but most ONLY come wiht a VGA cable.
You can lookup your specific monitor to find out.