I tried all the ports. Normally, I connect the monitor using Thunderbolt/DisplayPort mini connector which is on the laptop and it works well with full resolution. The problem is that this way, I can connect only one monitor and have to plug/unplug the cable too often which is inconvenient and I'm afraid about the port (two cables already broke, if the port on the laptop breaks as well, I'm in trouble).
So I would like to use docking stations ports (there are 2 displayports). I don't remember if I patched the framebuffer (maybe, some time ago, I tried everything), but should this be necessary when the monitor works normally using the laptop port?
The ports on the docking station still do not work. But now also the mini display port on the laptop doesn't work most of the time (strangely, sometimes it does work). When it does not work, the monitor complains that the laptop sends wrong resolution / timing / frequency / whatever. It is different than the docking station ports - for these, the correct EDID is detected, but the monitor goes sleep (without complaints). It seems to me that when the laptop mini display port does not work, the OS deals with the monitor the same way as with the internal display (for example, it offers the same resolutions in System preferences for the monitor as for the internal display).... Strange.