iTerm2 - zsh - keep history of commands when opening a new pane
To share history between sessions, you need to use the SHARE_HISTORY option.  Additionally, you will want to append, rather than overwrite your history file.

setopt SHARE_HISTORY
setopt APPEND_HISTORY


Per the ZSH documentation (Chap. 16 - Options) you should also disable INC_APPEND_HISTORY.


  This option both imports new commands from the history file, and also causes your typed commands to be appended to the history file (the latter is like specifying INC_APPEND_HISTORY, which should be turned off if this option is in effect). The history lines are also output with timestamps ala EXTENDED_HISTORY (which makes it easier to find the spot where we left off reading the file after it gets re-written). 


There's also a few other commands that you may be interested in to deal with your dupes:


HIST_NO_STORE - removes the history command from history.
HIST_IGNORE_ALL_DUPS - deletes an older version of added commmand
HIST_SAVE_NO_DUPS - when saving the history file, older commands that duplicate newer ones aren't saved