Do you know of any app/sw that shows cpu, gpu, etc temps/details on the taskbar? Something like CoreTemp but with more information. The closest thing I've seen so far is Rainmeter using hwinfo but the numbers are overlaid on the desktop wallpaper.
Somewhat adequate at stock settings unless you live somewhere with high ambient temps. But if you overclock, it's the first thing you'd need to change.
Compared to others... It beats other stock cpu coolers but aftermarket coolers will be better.
Seems like a standard modem/router so I'm guessing no. If you have a long enough ethernet cable, you can connect it to the first router and use it as a second wireless access point.
You shouldn't have to do much for a brand new card. Do you use Firestorm or Afterburner to set the fan curve or just let it run stock? If no, I would ask for a replacement.
Save up a good amount because if you upgrade the cpu (assuming ryzen is your goal), you need to upgrade your motherboard as well.
And I would upgrade the cpu first.