From my reading, many respiratory illnesses can cause these symptoms, but right now if you have a respiratory illness at all, odd are it's COVID-19, so it's worth at least getting a PCR test. And if it's not that, you have a very serious flu or something which probably requires treatment as well.

You are right, I had similar data and same warning as I got for COVID-19 from Oura cca year ago with regular flu. It is now more important because of COVID-19, but it is also very helpful for any similar illness that one may spread.

There are lots, as what you really are measuring are subtle variations in the sympathetic and parasympathetic drives of the heart by the autonomous nerve system. This can get affected by lots of things, a quick googling provided dozens of completely different papers looking it stuff like heart disease itself, but also clinical depression etc.