Yes on the first question. You need to extend the desktop (which should be the default when you plug in the extra monitor), then arrange them to match their physical positions.
I don't see FreeSync on only one screen being a problem. You need to run a game fullscreen to use it anyway, so you won't be interacting with the second screen (though it should remain visible and refreshing normally). But I can't answer definitively, since I haven't used the feature.
Yes to the 1st question.
For the 2nd question, Freesync (adaptive sync) only works on the DisplayPort. It will work fine with a supported monitor while the 2nd monitor is on DVI/HDMI.