Macos – iTerm2 hotkey window activates non-hotkey windows

Yes, as long as you have version 3.0.0 or later (or pre-release versions). If you go to the "Keys" tab in iTerm2's preferences, you should see the "Hotkey window hides when focus is lost" checkbox in the "Hotkey" section. Uncheck it.

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)