No complaints, the timing worked out just fine.

As long as your paste spreads fine, you should be okay. If you are concerned, buy more. It's only a few bucks.

https://pcpartpicker.com/list/HCZn3w

I threw your parts into here for just an idea of what you had. Assuming you don't have a ton of drives or a 300w video card in your system, you are probably fine. You should add the rest of your parts in the link I provided to confirm you aren't approaching 80% of your available wattage.

You should be able to get away with that cooler. See if you can find the thermal properties of your cooler. If not, you can find a suggested replacement on PCPartPicker, but you should look deeply into whatever you purchase and try taking measurements to confirm it will fit.

Finally, PCPartPicker suggests a bios update before you swap processors, just in case your bios is old and doesn't support that chip.