You're putting too high a bar on what we need to understand. We don't understand physics in its entirety either- we can still say lots of things with confidence.
That we are our physical body is pretty certain. You press a certain part of the brain, and predictably our personality changes. Of course we can't be certain of a lot of things, but I am much more certain of this than I am of of other things, and Godels theorems don't apply.
I also supect this, but let's be honest that we as a species are not close to understanding consciousness in it's entirity yet so I'd refrain from making such absolute statements