I ran into a possibly related issue with z-fighting on my Intel HD 3000 GPU running under Windows 7. Seems like the same issue you had with #1 and #2 there.
In our game (which is first-person) 1 unit = 1 meter, so the default near clip of 1.0 was way too close. Setting the near clip to 0.01 results in terrible z-fighting. 0.1 has the same problem but it doesn’t happen until the objects are about 10 times as far away, and this ended up being our “happy medium”. Adjusting the far clip plane does not seem to have any effect on the problem, though we need to have it set to a specific value (350) anyways.
This only happened on the Intel GPU running on GL. The same GPU running on DX9 had no such problem. Also the discreet NVIDIA GPU had no problem in DX9 or GL.