Hi Steps,
I own the same meter...and Yes, I've experienced this. Yes i think its pretty much normal..
but first, lets make sure your meter is ok....you can do this by using a very short piece of wire to short the input. if it becomes relatively stable, then, your meter is not doing anything unusual.
i found that some leads, at low resistance, will vary widely with just the slightest movement of the wire, and being high impedance, it picks up nose quite easily. If your making low voltage and low resistance measurements accurately can be a challenge ...voltage measurements that low, consider using leads that are shielded.
for low resistance..i've assumed that because the leads are stranded, that simply by moving the leads the overall resistance can change slightly. I've set up testing rigs to make sure noting mvoes when doing low resistance measurements. ... though I find using an old-fashioned whetstone bridge a much more accurate way to measure very low resistances.
as far as offsets go, there is a rel function on the meter. that's how i deal with the resistance offsets.
unconnected, yea the reading jumps wildly, though this is something i have observed with many meters.
i can get my shorted voltage to read 0.0000 when i am using shielded leads with a banana to bnc adapter, and ensuring the bnc shield is on the ground side. pamona makes the banana to BNC adapter i use. This also helps with low resistance stability, however, the resistance of my coax leads is much higher than my standard test leads.
also, there is a filter feature, which averages over x number of samples. this is also a good feature to make use of. unless you are running off a lead acid cell, there is noise on most DC lines, and with the fast sampling rate of the meter, its gonna pick up varying voltages. the filter feature smooths those out. it doesn't do that automatically as they have no idea of your need, most of the time though, for normal measurements, you want the filter on.
hope that helps some... if you need more details, i can make a video or take some pictures.