NXZT has a good factory paste, never had an issue with it. And most pastes within $15 generally have the same performance, so any really. The differences, like I said are a few degrees centigrade cooler, but that does make a good difference if you plan on overclocking your CPU. where the temperature could be the same as a stock speed processor.
The cost is really minimal compared to the possible benefits you'll receive. People report that under full load, a good thermal paste (which you can pick up for less than $15) helps keep their CPU a few degrees centigrade cooler, which is always a plus.
Good news! No, you will not. The motherboard comes with an on-board ethernet adapter which, when built, will be on the back of the case. So case closed!
For future reference, when you're checking out motherboards, look on the left side under specifications, and check for the section 'Onboard Ethernet.' It being present signifies you'll find an adapter on the motherboard.
Also, the secondary 1080 you linked is actually a bit better than the one in the default build, so definitely, it will do.
*Edits for spelling, derp.