Is this PC build good for 1080p gaming and streaming in high settings? And are the pieces really compatible?

Solution
Gtx1080 is overkill , Gtx1070 can hadle 1080p gaming without stress.
You could move that to r5 2600x, faster ddr4.
And use stock cooler over 212, only 3~5c difference


A ryzen 2600(x) will be better since you are streaming. A gtx 1070(ti) depending on how close the price is will do more than fine.
Also that thermalpaste is not needed since the stockcooler comes with it.
Faster ram would help the ryzen a lot (do keep it in a 2x4 kit).
Psu is overkill and a simple seasonic focus+ 550 w or supernova g3 550w is more than enough.
I would recommend a 250gb ssd in there it will really speedup useage and help when you run out of ram.
 


The only thing I'm not sure about is that ssd. Those started coming up out of nowhere on amazon but haven't really had a thurough testing yet. I myself would spend the 10$ extra and get an adata, kingston, sandisk,... drive but thats up to you.