Just a guess, but, for the first cottage, it does sound as though there was once an external chimney built up against the gable end. No idea why they should have wanted to remove it though.
With the old traditional chimneys, it was usual to have them reducing in width as they go up the wall. As it reduces, each "shoulder" would have had a slate course built in to shed rainwater out of the main wall and run out over the sticking out bit.
The last reduced bit would have had a horizontal course of slates right across it, again to throw rainwater off the main wall.
For the second cottage, the window arrangement is likely simply to reflect the way the rooms are arranged internally. With the stack, it would have been better (though more expensive) to have enlarged the main chimney to turn it into a double flue. It must look odd as it is now.