Cedrick Mapa

Yes, will work without issue.

I run a 2700x with a 2080ti. That should answer the old bottleneck question lol. Only time a cpu will bottleneck a high end GPU is at 1080p where the cpu is more often than not the weakest link as the GPU can easily soit out enough frames. This is true for easier to run games like csgo ect. 

Absolutely not.  
 
2070s is a 1440p/1440pUW card but isn't worth it due to the price/performance of the 5700XT.  5700XT would be better for 1080p tho probably a bit overkill, which leaves room for moving to 1440p.

CPU can easily handle the upgrade, I'd personally get the 2070 super for that extra performance jump and overclock it to the max and then you'll be right on the limit of what your system can handle cpu wise and psu wise 

Definitely shouldn't be any bottlnecks, a 2700 and 5700XT is a good combo. As for will it be a good upgrade, I would say yes. Userbenchmark rates the 5700xt as about 70% faster than the 580, so it should be a significant performance improvement, especially at higher resolutions. 

that's what im planning, already selling my unit in our market here. Hopefully it will be sold soon