1. First problem is one with resistor. It has to do with instrument having high impedance and on the edge of autoranging ... It does seem a bit nervous, but any meter can be destabilised this way if you try hard enough.
Yep. I bet it will disappear if you switch to manual ranging.
Of course it will, it is autoranging problem. You have value right at the edge of range, very high impedance on input and you're injecting maybe a volt of interference. That combined with fast frontend, makes a jittery autoranging.
We are all annoyed when things are not perfect, but it is not a real problem.
Also Dave's test with BM786 is invalid .. Of course that 60000 count meter won't have problem with 560 kOhm. It might have problem with 650 kOhm, because that is where it will have switchover and similarily high impedance.....
Later, I will try this with some meters, right on their switchover point, and high resistance mode.. I think many of those will have same problem, unless they have very slow autoranging, and very slow front end and sampling...