iTerm2 fullscreen causes an empty line at the bottom

Change the vertical character spacing in iTerm2 Fonts preferences and it should do the trick

See this answer, excerpted below. It was written about gnome-terminal, but it's the same for iTerm:

Terminal emulators work with a grid of cells: a whole number of cells both horizontally and vertically. That's why when you resize the window by dragging its corner, it resizes in unusually large steps rather than pixels. [...]

In fullscreen mode, gnome-terminal is forced to a size that's not a multiple of the size of its character cells. Utilities and applications running inside terminals have no notion of such partial cells and couldn't draw in the remaining area, it just doesn't exist for them.

You might want to experiment with different font sizes, you might find one where an integer number of cells just fit (or at least the gap is not that large)