With regards to GPU’s I thought I had issues with adding a 1080ti, the main thing is power. From what I remember of the 820 it’s likely to have a 1kw (1000w) power supply, then the next problem is power supply cables. The 1080ti needs 2 power connections a 6 way and an 8 way. As I had two cards only the 1080ti needed extra power connection. My box had two 6 way cables so all I had extra to buy was a 6 to 8 adapter cable. PCI 3 is good for cpu. So I don’t think you’ll have performance issues.
Be aware that the more you add to the PCI bus the more you interfere with the GPU, if you need power for a data ssd you’ll lose for you gpu
I was a bit worried about installing Ubuntu on a windows machine, but all went well. If it has windows already installed, install to a separate disk if you can. Then leave space in the windows partition for the swap. You can do this once Ubuntu is install, just install parted.
You can check HP for serial number maybe you have warranty left.